Virtual Helper


Any small thing looked at a greater depth have excellent structure or pattern behind them


My parallelogram law of forces

Philosophy of Mathematics

Is Mathematics really Hard?(specially for those who hate it).I have expressed my views regarding mathematics.How Mathematics is associated with all walks of human life.

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Web technology

Everything in the world is connected.This is another nice article related to div tag.

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Another webtechnology post

Funny illustration of webtechnology related concept.How web technology various branches associated with the human life

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Free Educational Video

Treasure Resources

All open resources Educational resources under one shell for all subjects .Don't forgot to bookmark this.

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Great indian who want to change our way of living



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best educational site for those who want to learn



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aptitude tips



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organized math video gems under one shell



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josephus problem solver for generalized n



#include<stdio.h>
int main()
{
int n1,n2,s=0,cnt,i,k;
printf("\n enter how many persons\n");
scanf("%d",&n1);
int a[n1];
k=n1;
for(i=0;i<n1;i++)
a[i]=i+1;
printf("\n enter every which\n");
scanf("%d",&n2);
while(k>1)
{
cnt=0;
while(cnt<n2)
{

if(a[s]!=0)
cnt+=1;
if(cnt!=n2)
s+=1;
if(s==n1)
s=0;

}
a[s]=0;
k=k-1;
}

for(i=0;i<n1;i++)
{
if(a[i]!=0)
printf("\n The %dth person is saved",i+1);
}
getch();
}
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this is for those who prepare for gmat



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best youtube channels for developing your computer knowledge from the scratch



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C program for playing tic tac toe



#include<stdio.h>
void assign(int **arr, int k)
{
int i,j;
for(i=0;i<k;i++)
{
for(j=0;j<k;j++)
{
arr[i][j]=0;
}
}
}

void display(int **arr, int k)
{
int i,j;
for(i=0;i<k;i++)
{
for(j=0;j<k;j++)
{
printf("%dt",arr[i][j]);
}
printf("n");
}
}

int input(int **arr,int m)
{
int k,i,j;
k=1;
scanf("%d%d",&i,&j);
if(arr[i][j]!=0)
{
printf("n the position has already occupiedn");
}
else
{
if(m%2==0)
{
arr[i][j]=1;
}
else
{
arr[i][j]=2;
}
k=0;
}
return k;


}

int play(int **arr, int k,int r)
{
int m=1;
printf("n please enter row(i) and column(j)>0 and <%d",k);
if(r%2==0)
{
printf("n player 1 enter your positionn");
}
else
{
printf("n player 2 enter your positionn");
}
while(m)
{
m=input(arr,r);
}
r=r+1;
return r;

}


int check(int **arr, int k)
{
int i,j,m=1,t,r=0;
int cnt1,cnt2,cnt3,cnt4;

while(m<=2)
{
cnt1=0,cnt2=0,cnt3=0,cnt4=0;

for(i=0;i<k;i++)
{
cnt1=0,cnt2=0;
for(j=0;j<k;j++)
{
if(arr[i][j]==m)
{

cnt1+=1;
}

if(arr[j][i]==m)
{
cnt2+=1;

}

if(i==j)
{
if(arr[i][j]==m)
{
cnt3+=1;

}


} //end of i==j

if((i+j)==(k-1))
{
if(arr[i][j]==m)
{

cnt4+=1;
}


} //end of i+j

} //end of j loop

printf("n value of m =%d",m);
printf("n cnt1=%d cnt2=%d cnt3=%d cnt4=%dn",cnt1,cnt2,cnt3,cnt4);
if((cnt1==k)||(cnt2==k)||(cnt3==k)||(cnt4==k))
{
r=1;
t=1;
break;
}
else
{
t=0;
}



} //end of i loop

// printf("n value of m =%dn",m);



if(r==1)
{
break;
}
m=m+1;

} //end of while
if(m==3)
{
m=m-1;
}
if(t==1)
{
return m+t;

}
else
{
return t;
}


}


int main()
{
int n,move=0,flag=0;
printf("Tic Tac Toe gamen");
printf("please enter the odd no for which square matrix has to be generatedn");
scanf("%d",&n);
if(n%2==0)
{
printf("please enter the valid odd no >0");
}
else
{

int i,j;
int **a=(int **)malloc(n*sizeof(int *));
for( i=0;i<n;i++)
{
a[i]=(int *)malloc(n*sizeof(int));
}

assign(a,n);
while(move<(n*n))
{

display(a,n);
move=play(a,n,move);
if(move>2)
flag=check(a,n);
printf("n flag value is %dn",flag);
if(flag!=0)
break;
}
display(a,n);
printf("n flag value is %dn",flag);
if(flag==0)
printf("n The game is draw");
else if(flag==2)
printf("n The player 1 has won the game");
else
printf("n The player 2 has won the game");



}
getch();
}
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C program for odd order magic squares generalized



#include<stdio.h>
void main()
{
int n;
// int i=0,j,k=1,a[15][15];
//clrscr();
printf("n Enter any odd number>1 t");
scanf("%d",&n);
if(n%2==0)
{
printf("This program works only for odd numbersn");

}
else
{
int i=0,j,k=1,a[n][n];
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
{
a[i][j]=0;
}

}
i=0;
j=n/2;

a[i][j]=k;

while(k<(n*n))
{
i=i-1;
j=j+1;
if((i<0)&&(j>=n))
{
j=j-1;
i=i+2;

}
else if(i<0)
{
i=n-1;
}
else if(j>=n)
{
j=0;
}
// else
// {
if(a[i][j]!=0)
{
j=j-1;
i=i+2;

}
k=k+1;
a[i][j]=k;

// }


}
printf("n the magic squares for given order isn");
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
{
printf("%dt",a[i][j]);
}
printf("n");
}



}


getch();
}
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helpful post which I came across(How to Detect Hidden Camera in Trial Room? )



credits to the original poster
How to Detect Hidden Camera in Trial Room?
In front of the trial room take your mobile and make sure that mobile can make calls........
Then enter into the trail room, take your mobile and make a call.....
If u can't make a call......!!!!
There is a hidden camera......
This is due to the interference of fiber optic cable during the signal transfer......
Please forward this to your friends to educate this issue to the
public......To prevent our innocent ladies from HIDDEN CAMERA...........
Pinhole Cameras in Changing Rooms of Big Bazaar, Shoppers Stop?
A few days ago, I received this text message:
Please don't use Trial room of BIG BAZAAR there are pinhole cameras to make MMS of young girls.
So, please forward to all girls. Also forward to all boys who have sisters and girlfriends.
Don't be shy in forwarding this message. Because its about protecting the integrity of all girls & ladies.
HOW TO DETECT A 2-WAY MIRROR?
When we visit toilets, bathrooms, hotel rooms, changing rooms, etc., How many of you know for sure that the
seemingly ordinary mirror hanging on the wall is a real mirror, or actually a 2-way mirror I.e., they can see you,
but you can't see them. There have been many cases of people installing 2-way mirrors in female changing rooms or bathroom or bedrooms.
It is very difficult to positively identify the surface by just looking at it. So, how do we determine with any amount of
certainty what type of Mirror we are looking at? CONDUCT THIS SIMPLE TEST:
Place the tip of your fingernail against the reflective surface and if there is a GAP between your fingernail and the
image of the nail, then it is a GENUINE mirror.
However, if your fingernail DIRECTLY TOUCHES the image of your nail, then BEWARE, IT IS A 2-WAY MIRROR!
(There may be someone seeing you from the other side). So remember, every time you
see a mirror, do the "fingernail test." It doesn't cost you anything. It is simple to do.
This is a really good thing to do. The reason there is a gap on a real mirror, is because
the silver is on the back of the mirror UNDER the glass. Whereas with a two-way mirror, the silver is on the surface. Keep it in mind! Make
sure and check every time you enter in hotel rooms.
Share this with your sisters, wife, daughters, friends, colleagues, etc.
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Note



என்னுடைய எழுத்தில் பிழை இருக்கலாம் ஆனால் என்னுடைய உள்நோக்கத்தில் பிழை இல்லை.
My words may go wrong sometimes but not my intentions
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தமிழ் காலம் (Recursion)



void kaalam(kaalam)
{
நேற்றைய எதிர்காலம் இன்றைய நிகழ்காலம் .
இன்றைய எதிர்காலம் நாளைய நிகழ்காலம்.
நாளைய இறந்தகாலம் இன்றைய நிகழ்காலம் .
kalam(kalam);
}
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program to find prime factorisation of a given number



you can extend the array as far you like by typing the prime numbers so that it will works for larger numbers
#include<stdio.h>
int main()
{
int a[]={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127};
int i=0,n;
printf("enter any even number for which prime factorisation has to be foundn");
scanf("%d",&n);
printf("n the prime factorisation of a given number is n");
while(n!=1)
{
if(n%a[i]==0)
{
printf("n%d",a[i]);
n=n/a[i];
}
else
{
i=i+1;
}
}
getch();
}
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Great site for true learners



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Good speeches



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Best youtube channel for those who want to learn french from novice to professional



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how to check the given number is a palindrome (using pow and log in a easy way)



#include<stdio.h>
#include<math.h>

void main()
{
int num,cnt,rev=0,temp;
clrscr();
printf("\n Enter the number\n");
scanf("%d",&num);
temp=num;
cnt=log10(num)+1;
printf("\n the no of digits in a given number is %d",cnt);
cnt=cnt-1;
while(num!=0)
{
rev=rev+((pow(10,cnt))*(num%10));
cnt=cnt-1;
num=num/10;
}
printf("\n the digits in reverse order is %d",rev);
if(temp==rev)
printf("\nThe given number is a palindrome");
else
printf("\nThe given number is not a palindrome");
getch();
}
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how to compute square root of a perfect square just using simple addition only



Caution: This methods works just only for perfect squares
#include<stdio.h>
void main()
{
int cnt=0,sum=0,i=1,num;
printf("\n Enter the number for which you want the square root\n");
scanf("%d",&num);
while(sum<num)
{
sum+=i;
i+=2;
cnt+=1;
}
printf("\n The square root of a given no is %d",cnt);
getch();
}
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Is Right is an Synonym for wrong or Right is an Antonym for wrong



This is just my own idea.So don't take it seriously.What is wright and what is wrong?.Is Right is right or wrong is wrong?
What the heck in the world is it mean?.You may think like that but in the end you will understood why is it the case.Every object has its own nature.Here the object which I refer may be person,place or thing and the nature refer to its behaviour,character or properties.The nature of the object in most of the times it is fixed.But it is the window through which we look differs.That's why for someone the event seems to be good and for others it isn't.Here the window which I am referring to here is your illusion.
This can be understood very well by taking an example from our epic called Mahabhartha.one time somebody asked Yudhisthira and Duryodhana the same question .But their answers are completely different. The question is go out and tell about what sort of people are out there in the world.Yudhisthira went and came back and he told that world is full of good peoples.There is nobody bad out there.similarly when Duryodhana went and came back he told that world is full of bad peoples .For some people the heaven seems to be hell and for others the hell seems to be heaven .
One more story which I want to mention is from an ( author named shivkhera) book called "you can win".In that one of the story I want to mention specifically.The story is as follows.
This is true when we consider a failure and success.When someone wins an competition to the outerworld that person got an success but that person only knows whether it is a success or failure for him and viceversa.So if you get failure in life consider this in your mind and hope that you have learned something from that.It means that you interpret failure as a starting point for your success.
once upon a time there was a man who is a father of two sons.The nature of the father is a drinker.The years rolled.After thirty years the two sons became grown up.In that one of them became rogue.And the other one became a district collector.Here the nature of the object(father) didn't change rather the viewers prespective changed(and here the viewers are two sons.).
Let us assume that if 20 people say that one thing is right among 25 people.Eventhough it may be wrong but in their universe(among 25 people) that may become right.Because the majority is always overriding the minority.It doesn't means that 20 people are right and the remaining 5 people are wrong.
We always love to be fooled by our illusions eventhough sometimes if we get an opportunity to overcome it. so your illusion rules you .And in general illusion rules our world which we live in. An illusion is a imaginary circle which we create ourselves and we want to live within it. But the great weakness can become a great strength if we fooled by it other illusion.(e,g like the complement of complement of the something is the original).
one more simple math example to understand this .suppose you solve a problem related to area or distance and while solving the problem let us assume that you got an quadratic equation and you are solving it.The answers are one root is positive and the other one is negative.you are verifying by applying them in the quadratic equations.Both are valid solutions .Eventhough both are valid solutions to the quadratic equations our answer should be in positive.Since the distance and area cannot be expressed in negative quantity.The context matter much more(here the context is problem definition).
Also you can feel this is very well true if I mention one more point.once I heard sukisivam talk.One time he mentioned that "a philosopher called osho told that "Words are mine and their meanings are yours".This is absolutely right.
In everything we are fooled by our senses .For example eventhough we know that in mp3 most of the things are cut out we are in illusion that we are getting an complete one.This is the same with video encoding and illusion will be our partner for our own life.If you say someone is sitting idle .It means are they really idle.If you say they are idle then means you are thinking (caption is used as name in visual basic)but in reality they aren't.Their biological part is always working.
Illusion has great power that has been understood by scientists and mathematicians.I want to mention one example.If something is very tough to prove in mathematics then mathematician will assume contradictory to the nature and that leaves to contradictory so the assumption is wrong like that he will prove.Here he used the power of illusion something which is not prevailed.
similar to mathematicians ,the computer guys have understood the power of illusion and they used its power to it's full length and they created a concept called view in the database.The views provides a great level of advantage.Actually view is a virtual table which does not exist in the database which can be computed or collated from data in the database.
More often the concept of illusion has been used in programming to achieve the reality.I have just given two or three examples to illustrate the power of illusion but illusion is associated with all parts of our life.

So what we think might be good in our universe may not be treated as good in other universe.so the context matters. why these stupid reasonings that I want to tell to you.Because I thought of introducing a new weird concept called p-adic numbers.In our universe the distance between 2 and 5 is greater than distance between 0 and 0.6(i.e 6/10)if we consider all the realnumbers from starting point to the ending point between the numbers.But this is not true in case of other universe called p-adic numbers in which the reverse is true . where p in p-adic stands for prime numbers consider this infinite sum 1+3+3^2+3^3+3^4+3^5+........... If I say the answer is -1/2(if you consider the 3-adic universe) you may tell that what the heck are you doing?
You may tell that it is wrong .But it is absolutely right when we consider the p-adic universe because our way of distance concept is shattered completely in this universe.
In order to understand this I will give an example related to computer science k="55"; j=72; what is k+j answer is not 55+72 as you may think .The real answer is 5572.It's the context matters plus generally stands for addition but in java and javascript it is not like that .plus may stand for addition or concatenation depending upon their components.If the two components are numbers then usual addition will be performed or when either one of them or both of them are string concatenation will be performed.
Last example which I want to mention you is that I want to ask a simple basic question what is an array?.You may say that it is an homogenous collection of elements.Again the context matters .This definition will be valid in strong programming languages like c,java.But this definition will fail in case of weak datatype languages like javascript where array can contain masala elements(where masala means mixed datatype )
Now you might ask then what the heck is mean that what is right and what is wrong?.
That's the heck I don't know. Simple things are not simple when you go in depth under it you may find the universe which has no end to it.
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another funny imaginary narration I came across



Credit to the original poster

A Computer Engineer's narration of Ramayana

This is just an imagination, pls dont take it seriously

This is a small riddle kind of a thing. Just imagine a Computer Engineer narrates Ramayana.

LAN, LAN ago, in the SYSTEM of I/O-dhya, there ruled a PROCESSOR named DOS-rat. Once he EXECUTED a great sacrifice PROGRAM after which his queens gave an OUTPUT of four SONs - RAM, LSIman, BUG-rat and SED-rughana.

RAM the eldest was a MICROCHIP with excellent MEMORY. His brothers, however, were only PERIPHERAL ICs. Once when RAM was only 16MB, he married princess C ta.

12years passed and DOS-rat decided to INSTALL RAM as his successor.However,Queen CIE/CAE(Kayegayee), who was once offered a boon by DOS-rat for a lifesaving HELP COMMAND, took this opportunity at the instigation of her BIOSed maid and insisted that her son Bug-rat be INSTALLED and that RAM be CUT-N-PASTED to the forest for 14 years. At this cruel and unexpected demand, a SURGE passed through DOS-rat and he CRASHED like unstable version of AI MSN does in intel.

RAM agreed to LOG INTO forest and C ta insisted to LOGIN with him. LSI-man also resolved on LOGGING IN with his brother. The forest was the dwelling of SPARCnakha, the TRAN-SISTOR of RAW-van, PROCESSOR of LAN-ka. Attracted by RAM, she proposed that he should marry her. RAM, politely declined, perceiving C ta to be his SOURCE CODE. She hastened to kill her but LSI-man cut her nossile PERIPHERAL. Weeping, SPARC-nakha fled to LAN-ka, where RAW-van, moved by TRAN-SISTOR s plight, approached his uncle MAR-icha. MAR-icha REPROGRAMED himself to form a golden stag and drew RAM deep into the forest. Finally, RAM shot the deer, which, with his last breath, cried out for LSI-man in voice of RAM s SOUND CARD. Fooled by this VIRTUAL RAM SOUND, C ta urged LSI-man to his brother said. Catching the opportunity, RAW-van DELINKED C ta from her LIBRARY and changed her ROOT DIRECTORY to LAN-ka.

RAM and LSI-man started SEARCHING for the missing C ta all over the forest. They made friendship with the forest SYSTEM ADMINISTRATOR Akshat sorry… SU-greev and his powerful co-processor Ha-NEUMAN . who agreed to help RAM. SU-greev ordered his PROGRAMMERS to use powerful SEARCH techniques learnt in GOOGLE to FIND the missing C ta. His PROGRAMMERS SEARCHED all around the INTER-NETworked forests. Many tried to EXCITE the birds and animals not to forget the WEBCRAWLERS (Insects) and tried to INFOSEEK something about C ta. Some of them even shouted YAA-HOO but they all ended up with NO FOUND MESSAGES Google, Lycos nothing was left untouched. The only thing they forgot was to mail iitcse01 & get PTI s help. Ha-NEUMAN then devised a RISCy TECHNOLOGY and used it to cross the seas at an astonishing CLOCK SPEED. Soon Ha-NEUMAN DOWNLOADED himself into LAN-ka. Ha-NEUMAN found C ta under a brown - green (as Brahma will call it) TREE STRUCTURE Ha-NEUMAN used the LOGIN ID (ring) to identify himself to C ta. After DECRYPTING THE KEY, C ta asked him to send STATUS_OK MESSAGE to RAM.

Meanwhile all raakshasa BUGS around C ta captured Ha-NEUMAN to DELETE him using everything including Ctrl-Alt-Del. But Ha-NEUMAN spread chaos by spreading VIRUS Fire . Ha-NEUMAN pressed ESCAPE from LAN-kaand & conveyed all the STATUS MESSAGES to RAM and SU-greev. RAW-wan decided to take RAM head-on. One of the RAW-wan s SUN almost DELETED LSI-man with a Brahma -astra. But Ha-NEUMAN resorted to some ACTIVE-Xgradients and REFORMATTED LSI-man. RAM used the SOURCE CODE secrets of RAW-wan and wiped out RAW-wan’s presence on earth. Later, RAM got INSTALLED in I/O-dhya and spreaded his USER FRIENDLY PROGRAMS to all USERS and everyone lived happily ever after, playing & enjoying.

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What is the meaning of fancy word named code optimization(explained with Buddha principle)



I actually heard this talk from sukisivam and I thought of associating it with topic called code optimization.I think everyone have heard about Buddha.If not google it . Now let’s get into the discussion .The discussion is as follows “once a man asked Buddha guruji everybody telling that you have attained something great.Could you tell me what you have actually attained for that Buddha told that “I have not actually attained anything rather I actually left the unnecessary things which are minimum to retain the supreme thing”. Do you know why the word retain is used instead of attained since it is there with us but the junk seems to be dominating it which has be to be filtered or cleaned in order to retain the information( like data mining) This word has much more powerful meaning than you think. This principle not only applied to programming it can be applicable to various scenarios(example in case of database normalized database is the best one).I am pointing to a specific scenario here called programming.This is the principle that every programmer wishes to attain it.Everybody can do a program.But it doesn’t mean that it is efficient and readable one.Only a few can achieve it in action by applying the Buddha principle.
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All free legal e- books avaialable on this site



Hope this may help you.I hope most of them will be interesting to you.
http://www.getfreeebooks.com/
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best youtube channels and sites for those who want to learn computer science



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Is Quantum mechanics really weird?(simple and easy explanation )



Sorry for some funny things .These are my own ideas. During the explanation you make think that I am going out of the topic but while you finish reading the entire post everything will makes sense.Also one more thing I want to say before entering the topic All are equal in intelligence God has given equal intelligence for all.then why some people can easily grab the concepts while others are not.The answer is very simple since the people who are intelligent ( sorry for using the word intelligent ) people they have found an easy way to grab the concept.

Some concepts are intuitive and weird means they are not incomprehensible.It means that you have not found a way to make sense out of it.It does means they can’t be understood by any people.Things which may seems simple are not really simple.If it seems simple means you have not looked at in different directions.When you look at the same problem in different directions you can see some interesting and intricating ideas.This is true for learning also.The ability may differ for some people but everyone is entering into the sea .

Is normal things are normal ,similarly abnormal things are abnormal ?Ans:The answer is No.Humans are always fooled by their intuitions(this answer will make sense at the end) Quantum mechanics is a kind of physics where people go at atom level and they observe something with the help of it they are predicting something related to the universe.Their predictions are much more counterintuitive when they keep on going much more smaller level.But is this really valid?.This is the thing I am going to explain with a simple example of numbers concept.

Oh! Sorry for saying the word simple for numbers.Because in reality we know numbers are not simple as we think.These are not just digits .They are real valid objects.Since you have no identity on your own.You are recognized by the society by the associated number you have like social security .they have just 10 digits but how they are able to rule the world compared to the alphabets of the language.English has 26 alphabets but japanese and some other languages have more than 6000 or more alphabets .why they didn’t win the battle with the numbers .The Answer is very simple .Actually I have told you the answer .The answer is the question itself.Isn’t it funny?.since in order to say that itself I have used an associated numbers .So everything in the world can be just decrypted by numbers.

Why quantum mechanics makes sense.I am going to explain with the philosophical concept associated with the number theory concept called cantor set.Since when infinity enters the battle philosophical things will come into action.okay lets get into action.

Cardinality is the number of elements in the given set .

e.g consider a set A={1,2,3} ,B={a,b,c} .The cardinality of A is 3 and that of B is 3.

Cantor said that the cardinality of these two sets {1,2,3,4,5,………………….} and {2,4,6,8,10,12,14……………} are equal.

Similarly we can say that {1,2,3,4,5……….} and {1000,1001,1002,1003,1004,…………..} are equal .So we can find the numerous examples like this when infinity enters the battle . Why the cardinality of the following sets{1,2,3,4,5…………….} and {2,4,6,8,10………} and {100,101,102,103………} and {1000,1001,1002,1003……..} are equal?

Are they really equal?What is happening at the backend.

Answers are simple and interesting but before that we need some prior definitions.

Discrete values: Anything that can be listed are called discrete values.e.g integers,rational numbers etc…so when we say integers we are looking at a isolated points on the real number lines . similarly for rational numbers case but you have to go depth in order to understand it.Since when you consider an interval example[0,1] the middle point gives another rational numbers for an infinite times .It does not means that they are completely dominating on the real line.But there are numbers called irrational numbers which are like microorganisms which are really dominating the real number line.They are the rulers of the real number line.Consider some basic biology terms dominant and recessive for fun.so that you can appreciate the beauty behind it.

Continuous values:Anything that can’t be listed are called continuous values.e.g [0,1],[1,2],R etc….but in case of continuous values you have never able to list them even if you take your full lifetime or the time of universe.You can’t even able to list the numbers within an interval within[0,1] itself.The cardinality of R and [0,1] are same.

If you know the limit concepts in calculus then recall it otherwise leave it .This will help you to make much more sense.But I will do it with simple examples than these intuitive concepts.

So we can see that natural numbers ,integers,rational numbers can also be listed so they are called as countable set .In simple words anything that is discrete can be listed so that they can be paired with others sets that are listed like these.why I told you to recall the limit concepts some things can be listed easily some requires little intelligence.

First I will explain in a cantor manner .And then in a childish way by me.Cantor said that any two sets that can be listed with another are countable .The two sets that can’t listed with one another are called uncountable(means there are different size of infinity)



So we can see natural numbers are countable.Similarly for integers
Now we can say that we can’t make pair with integers.so it can be said uncountable.This is what I said previously you have to look in all possible directions since we matched 1 with 1 and 2 with 2 and this is an infinite set we will number come back so we are not able to list the ordered pairs .It does not mean that it can’t be done .Now



We got the answer with the simple logic called oscillation between positive and negative numbers .So we can list now .so they are countable.similarly this holds true for rational numbers .

But now we got he question are all sets are countable no it is not consider a set between [0,1] with natural numbers .you can’t do a mapping like the prevous ones .why since you can never can list all the the numbers between 0 and 1. Cantor explain this with this simple cantor diagonalization proof which is very simple.

Suppose you have listed the three numbers(consider 3 for example)0.255356….0.34555891…0.6589…….

These are the numbers that you have listed and you are saying that you have listed all the numbers .then I can create a new number which is not in your list by looking at a diagonal unit matrix 0.357…..(3 replaced for first decimal no in first no and 5 for second decimal no in second no and 7 for third decimal no in third no).

Now my childish explanation consider a sphere of radius (conisder for example laddu)with small size and big sizes . now you can list them in pairs with one to one



In this way when you are pairing you do not give matter to big sizes mapped with small sizes ..Also it is discrete you are able to list them.

Now for funny visualization put into grinder and make a powder as possible as you can do now you can see that you are not able to list them so one-to-one matching is not possible .Also one more thing we can observe that sphere with big radius will obviously provide more powder compared to sphere with small radius.In this way we are unintentionally giving importance to sizes.This leads to a conclusion that there are sets which are not countable and also among them there are bigger sizes of infinity are there.why you are not able to list them because they are continuous.

Also this can be done with the simple graphically

e.g for {1,2,3,4……} and {2,4,6,8….} y=2x functions but defined only for isolated points


Which is a straight line for any given x value you can always find an corresponding y values.Similarly for {1,2,3,4……….} and {….,-4,-3,-2,-1,0,1,2,3,………} are as follows


When you look at graphically it will look like this .So now we can easily verify the cantor concept with a simple test called horizontal line test.

Horizontal line test:To determine whether the function is a one-to-one.Draw a horizontal at each solutions whether any other one more solution has been found on the horizontal line drawn.In this case and previous case which is no way possible so these are one-to-one function.


Before arriving to the conclusion one more simple example to understand it very deeply .why the word one-to-one function is very important .what role does it plays in the cantor’s concept.
Note:It is very important to analyze the defintion from nook and corner .Each word you consider unimportant may play a crucial role like the word here one-to-one.How depth you are going that is important that can decides your level of understanding of that concept especially this is true in case of mathematics.For you 0.9,0.99,0.999,0.9999..... all these may be equal but for a mathematician it is not.
you may leave it and put the number like 1 but behind it whole universe is arising that you can realize it's depth when you study only analysis and calculus at a greater depth.


Consider squares and square root of a number and as well as cube and root of a number
















As we can see the y=x^2 function since it is not one to one it does not cover the whole range so it’s inverse function is not defined for negative numbers where as in case of cube and cuberoot function that problem did not arise since it is one-to-one function.So it’s inverse function has values for all numbers including negative numbers.







So now we atlast arrived at the conclusion(moral of the story).the interval [0,1] is o neglible compared to the size of [-R,R] but we can get an complete idea about the universe of numbers by just taking a neglible part of it .Similarly quantum mechanics is valid .Actually the [0,1] is not a neglible part it is as same size as R .so studying the [0,1] means we are indirectly studying the entire real number line(entire universe of numbers)similarly this holds for quantum mechanics .scientists who are studying atoms and much smaller level are indirectly studying the universe.Everything in disguise.We have to come out of our ignorance in order to understand the reality.why is this because as albert Einstein said the two things are infinite. One is universe and another one is human stupidity .There is question about universe whether it is finite or not.But the second one is valid I think so.
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physics



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my scriblings



beauty of nature simple things are not simple since we are taking most of the things for granted but when we dive into it we can see that behind it's extreme complexities are there. A painter know the value of a painting and archaeologists know the value of an antiquities and a sculpture know the value of a statue and similarly a mathematician known the value of numbers,patterns and shapes. We can see it but they can observe it.
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This site is for those who want to study mathematics at a greater depth



http://www2.latech.edu/~schroder/fund_videos.htm

http://www2.latech.edu/~schroder/DE_videos.htm

http://www2.latech.edu/~schroder/comp_var_videos.htm

http://www.learner.org/courses/mathilluminated/

http://blossoms.mit.edu/library.html

http://www.math.tamu.edu/~scarboro/

http://www.adjectivenounmath.com/id85.html
http://online.math.uh.edu/Math1313/
http://www.onlineuniversities.com/blog/2008/11/100-awesome-ivy-league-video-lectures/
http://www.onlinedegree.net/50-best-blogs-for-math-majors/

http://www.ima.umn.edu/videos/

http://www.isallaboutmath.com/index.aspx

http://www.ictp.tv/diploma/index07-08.php?activityid=MTH

Ted Chinburg algebraic number theory semester 1
http://www.math.upenn.edu/~ted/620F09/hw-620SchedTab.html
semester 2
http://www.math.upenn.edu/~ted/620S10/hw-621SchedTab.html
semester 3
http://www.math.upenn.edu/~ted/720F10/hw-720SchedTab.html
semester 4
http://www.math.upenn.edu/~ted/721S11/hw-721SchedTab.html
http://www.youtube.com/TheCatsters
http://www.extension.harvard.edu/openlearning/math222/
http://math.sfsu.edu/federico/teaching.html
Miles Reid's lectures on Algebraic Geometry and Algebraic Surfaces.
http://www.mathnet.or.kr/new_VOD/sub1.php?key_s_title=Lectures+on+Basic+Algebraic+Geometry+by+Miles+Reid+%28WCU+project%29
http://vod.mathnet.or.kr/sub1.php?key_s_title=Lectures+on+Algebraic+Surfaces+by+Miles+Reid+%28WCU+project%29
Geometric Representation Theory Seminar - Fall 2007 by John Baez and James Dolan
http://math.ucr.edu/home/baez/qg-fall2007/

Summer School in Arithmetic Geometry

http://www.uni-math.gwdg.de/aufzeichnungen/SummerSchool/

Lectures on Real Analysis

http://courses.bilkent.edu.tr/videolib/course_videos.php?courseid=12

The Fourier Transform and Its Applications, taught by Brad Osgood at Stanford.

http://see.stanford.edu/see/lecturelist.aspx?coll=84d174c2-d74f-493d-92ae-c3f45c0ee091

David Forney's course on Coding Theory at MIT.

http://videolectures.net/mit6451s05_principles_digital_communication/

Differential Equations, taught by Arthur Mattuck at MIT.

http://videolectures.net/mit1803s06_differential_equations/

Tim Gowers - Computational Complexity and Quantum Compuation

http://www.sms.cam.ac.uk/collection/545358
http://sites.google.com/site/yourmathvideos/

http://numericalmethods.eng.usf.edu/
calculus in depthhttp://www.youtube.com/user/GRCCtv#p/search
http://mathispower4u.yolasite.com/
http://www.understandingcalculus.com/
http://www.natures-word.com
http://math.stackexchange.com/questions
best mathematical you can ever find out
http://www.ams.org/samplings/feature-column/fcarc-home


http://betterexplained.com
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collection of nice Math jokes



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Best video math treasure resource for you



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fractals ideas explained in a very clear manner



This is the best video you can ever see to get the math behind the fractals




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Best Animated Math tutorials



simple to complex ideas presented in an innovative manner http://www.whyu.org/

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Most popular MIT seminars



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Best youtube channel for advanced complex ideas



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Great mathematicians interviews and realtime math applications



Here some of great ideas that can change your way of thinking Also in the site mentioned andrew wiles (famous mathematician) who solved 350 years problem fermat's last theorem is also present .Enjoy it. http://www.claymath.org/video/


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Get clear ideas about all computer concepts and languages in tamil



Youtube channel for most concepts and languages in tamil(don't leave these treasures unnoticed)
http://www.youtube.com/user/reach2arunprakash


Another youtube channel in tamil(only for j2ee)

http://www.youtube.com/user/VIGNESHD57#p/u
for java
http://www.youtube.com/user/irkannan1981#p/u
http://www.youtube.com/user/irkannan1981#p/u
more computer concepts in tamil

http://www.youtube.com/user/sujeshanto#p/u
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Finite minds determining the nondeterministic infinite things



we see but mathematicians observe
There is a drastic difference between seeing and observing .The difference is,seeing means looking at a shallow manner without diving but observing means diving into it and then telling it.
Mathematicians are best virtual divers .They plunge into the world of abstract mathematics and they atlast come to the conclusion .
Here one more thing that I want to mention it,mathematics subject itself is a fractal,when you dive into it you can see that you are again at the top layer no matter how many layers you go into it .Mathematics is a subject where suprises hidden within suprises.Mathematics possess beauty which has no end to it.
I will explain this with some simple examples
Suppose consider the sum of infinite series 1+1/3+1/6+1/10+1/15+…..
Here you can see what the above numbers they are the reciprocals of nth triangular numbers.
When n=1,n(n+1)/2 gives 1
When n=2 , n(n+1)/2 gives 3
When n=3 , n(n+1)/2 gives 6
When n=4 , n(n+1)/2 gives 10
And so on .
Ok now you know where each denominator came from .
Ok when we see this infinite series we are unable to predict the sum of this infinite series but this can be solved this in simple algebraically.
First algebraically we will solve it
Let s=1+1/3+1/6+1/10+……………….
Now multiply both sides by ½
(½)s=1/2+1/6+1/12+1/20+…………….
Now with the help of simple logic ½ can be written as (1-1/2) and similarly 1/6 can be written as(1/2-1/3) and 1/12 can be written as (1/3-1/4) and so on.
=>(1/2)s=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+…………..
So all the terms will cancel except 1
So (1/2)s=1
=>s=2.
=>1+1/3+1/6+1/10+……………….=2
Hey hey wait one minute now consider
S=1+1/3(part of this infinite series and compute it in the same manner)
=>(1/2)s=(1/2)+(1/6)
=>(1/2)s=(1-1/2)+(1/2-1/3)
=>(1/2)s=1-1/3
=>(1/2)s=2/3
=>s=4/3
So now considering the finite sums like these you may tell that 1 and the last number will also remains .
So which implies you are seeing whereas mathematicians know last term will diminish when we are considering the infinite series since they are observing(How the last term diminishes .Answer is very simple in case of infinite series the last term will be a very big number reciprocal which is nearly zero .)
Ok now consider the another series 1+1/2+1/3+1/4+1/5+………..
Which is nothing but reciprocal of the sum of the natural numbers .by considering the previous sum of series we may tell that sum of the series might be some finite number which is not happening in reality.
We will see why it is
S=1+1/2+1/3+1/4+1/5+……………..
s=1+(1/2)+(1/3+1/4)+91/5+1/6+1/7+1/8)+(1/16+1/16+1/16+1/16+1/16+1/16+1/16+1/16)+……………
We are grouphing in terms of 2 power n and also note that
¼<1/3 and 1/8<1/5,1/6,1/7 and 1/16<1/15,1/14,1/13,1/12,1/11,1/10,1/9 and so on …..
>1+(1/2)+(1/4+1/4)+(1/8+1/8+1/8+1/8)+……………….
=1+(1/2) +(1/2) +(1/2) +(1/2)+…………..
So the infinite (1/2) terms quickly diverge to infinity (means they will turns to a huge number) so the subset itself diverges
So the original series 1+1/2+1/3+1/4+1/5+………….. diverges to infinity(very big number ) which is counter intituitive.
Now another example
Find the value of

Which we can’t predict it value since we are seeing but where as mathematicians are observing using simple algebraic operations we can able to find out its value. Actually the value is very interesting and it is called golden ratio(1.608..) which has pretty interesting features. Similarly one more example
Find the value of

Which can also be solved very easily using simple algebraic operations and geometric series help we can see that its value is 3
So We can see that finite mind(mathematicians) can determine the infinite intrinsic beauties.
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Theorem:Everybody loves mathematics (proof by contradiction and mathematical induction)



Proof: Mathematical induction is a fancy word which means given fact is true for all natural numbers
Contradiction is a fancy word which means that we will assume wrong to the statement which has to be proved and we will proceed while doing this we will be slipped to a loop hole where it will fails so which leads to the situation assumption might be wrong .Hence the statement might be true.
That’s ok .Now continue to the discussion. When n=1
Here 1 is a single person .let us assume that person is me .so we have to prove for the single person(here for me).So in order to prove the above theorem we have to prove the short lemma
Lemma :I love mathematics
Proof by contradiction :
So we will assume I hate mathematics.
Again in order to prove this lemma we have to use another short conjecture
Conjecture:Each person in the world is addicted must be addicted to something.That thing may be a music,person(boy or girl),money,gold etc.(this is also true for saints where they want to attain mukti or whatever may be)
So according to this conjecture I must be addicted to something.
Let us assume that thing may be music .
Eventhough I am in love with music only I am indirectly loving a part of mathematics associated with it.
Since the music produced by violin,clarinet,or a person atlast it will be in the form of a wave .so which implies that I am in love with specific transformations produced by them
So which leads to a contradiction.so our assumption is wrong.Therefore it implies that I love mathematics.
So we have proved for n=1.
So let us assume that the above statement (everbody loves mathematics) is valid for n=k.(here k is nothing but k persons)
So we will prove it for n=k+1
Since k+1=k +1
Since the statement n=k persons and also for n=1person has been already proved by us
So n=k+1 is true.
In order to understand this simple number theory concept may help you.
If 6 is divided by 3 and 9 is divided by 3 which implies that their sum is divided by 3.
Hence the theorem is true
That is everybody loves mathematics
Still if you are saying I hate mathematics then it means you are pretending like girl’s attitude,which means that in their terminology I don’t like it means I like it.
Anyway for some people relationship is visible(in terms of c language pointer to a variable) and for some people the relationship is just hard to see(in terms of c language pointer to a pointer to a pointer).
e.g

point p has a direct relationship with a circle which can be clearly seen.
Point p has no direct relationship to a circle which does means that it has no relationship at all.
Since both must be in a space ,through that space they are related.
In the above concept mentioned circle is the mathematics and the point is the thing and the relationship has been provided by observer.
Hope you understood
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All that glitters is not gold(proof using mathematics)funny mathematics



Proof:consider the following three functions Check whether they are identical
When we perform simple algebraic operations we can easily see that three of them are same that’s an illusion . Really the domain part for three of them are different . First for function f(x) , x values can’t be negative so it’s domain is x>=0 Second for function g(x), x value can’t be zero( since there is a hole at x=0) But for the third function all the values are allowed. we can see this difference clearly when we saw it in terms of graphically

So don’t judge by external appearances and fall into a trap. Moral of the story : Think in terms of mathematics before you take any action (hahahaha)
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one of the Best math site (nobody can explain as simple as(especially calculus) he does)



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khan academy in tamil



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stay hungry stay foolish apple steve jobs impressive talk



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video for those who want to get ph.d ,engineering and doctor and more(funny but meaningful one)



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cambridge videos (great ideas to change your way of thinking)



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helpful youtube channel for those who want to improve their english



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some more excellent gems of mathematics and physics



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Another youtube channel for those who want to learn math from scratch



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Another treasure house (youtube channel) for all college courses (but knowledge of hindi is necessary)



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some excellent youtube channels for mathematicians



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Another best site



this is the site to be bookmarked for those who wish to study mathematics along with physics
http://www.lucideducation.com/index.php
and one more best site for those who wish to know the mathematics behind fractals in an easy and best way
http://www.youtube.com/user/fractalmath
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Best site to get lot of useful informations especially for younger generations



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Best videos for mathematicians



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excellent site to improve your knowledge in a variety of fields



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For those who want to know how does google work



http://www.portfolio.com/images/site/editorial/Flash/google/google.swf
Hope this is a place where you can get the answer
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Where our education system is lacking?Find what should be done to rectify this



Must watch video for everyone for all ages
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For those who want to crack iit jee exams



This is a greatest helpful youtube channel which helps you to crack iit jee successfully.
http://zookeepersblog.wordpress.com/iit-jee-ipho-apho-physics-mathematics-videos-for-std-9-to-12/
http://www.youtube.com/user/dezrina
example video
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This video is for those who want to come up in their life-real time working example



part1

part2

part3
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Another Funny story with great moral which I came across



When I studied this story it reminds me of a movie called Ramana
Where to Tap Knowledge – Very nice
Ever heard the story of the giant ship engine that failed? The ship’s owners tried one expert after another, but none of them could figure but how to fix the engine. Then they brought in an old man who had been fixing ships since he was a youngster. He carried a large bag of tools with him, and when he arrived, he immediately went to work. He inspected the engine very carefully, top to bottom. Two of the ship’s owners were there, watching this man, hoping he would know what to do. After looking things over, the old man reached into his bag and pulled out a small hammer. He gently tapped something. Instantly, the engine lurched into life. He carefully put his hammer away. The engine was fixed! A week later, the owners received a bill from the old man for ten thousand dollars. ”What?!” the owners exclaimed. “He hardly did anything!” So they wrote the old man a note saying, “Please send us an itemized bill.”

The man sent a bill that read:

Tapping with a hammer …….. $ 2.00

Knowing where to tap ………… $ 9998.00

Moral: Effort is important, but knowing where to make an effort in your life makes all the difference.
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Motivational Moral Story another story which I came across



Farmer & the Donkey – Motivational Moral Story
One day a farmer’s donkey fell down into a well. The animal cried piteously for hours as the farmer tried to figure out what to do.Finally, he decided the animal was old, and the well needed to be covered up anyway; it just wasn’t worth it to retrieve the donkey.He invited all his neighbors to come over and help him. They all grabbed a shovel and began to shovel dirt into the well. At first, the donkey realized what was happening and cried horribly. Then, to everyone’s amazement he quieted down.A few shovel loads later, the farmer finally looked down the well. He was astonished at what he saw. With each shovel of dirt that hit his back, the donkey was doing something amazing. He would shake it off and take a step up.As the farmer’s neighbors continued to shovel dirt on top of the animal, he would shake it off and take a step up. Pretty soon, everyone was amazed as the donkey stepped up over the edge of the well and happily trotted off!

MORAL :
Life is going to shovel dirt on you, all kinds of dirt. The trick to getting out of the well is to shake it off and take a step up. Each of our troubles is a steppingstone. We can get out of the deepest wells just by not stopping, never giving up! Shake it off and take a step up.
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100 Informative & Inspiring YouTube Videos for Educators



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13 minutes video that will show how one should face the life and live like a legend




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Biggest Motivational video you can ever see in the internet-No more than this is needed



Disability is not on your body it's on your thought .
Video that will help you to rewrite and reinvent your life

and one more
http://www.youtube.com/watch?v=a8Cwx2UbTJA
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some quotes about failure which I can't forgot ever



Truth of the Failure .....!!

Failure doesn't mean you are a failure...... it does mean you haven't succeeded yet.

Failure doesn't mean you have accomplished nothing..... it does mean you have learned something.

Failure doesn't mean you have been a fool...... it does mean you had a lot of faith.

Failure doesn't mean you have been disgraced...... it does mean you were willing to try.

Failure doesn't mean you don't have it...... it does mean you have to do something in a different way.

Failure doesn't mean you are inferior...... it does mean you are not perfect.

Failure doesn't mean you've wasted your life..... it does mean you've a reason to start afresh.

Failure doesn't mean you should give up...... it does mean you should try harder.

Failure doesn't mean you'll never make it...... it does mean it will take a little longer.

Failure doesn't mean God has abandoned you...... it does mean God has a better idea!
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This is called life(a living legend)(A true man who discovered the real meaning of life)



Witness - Super 30 - The First Step - 13 July 08 - Part 1

Witness - Super 30 - Hard Lessons - Part 2

Witness Super 30 Special - 08 Oct - Part 3

Witness - Super 30 Special - 17 July 08 Part 4
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I received this as a email-hope it would be nice to post



1. If you see children Begging anywhere in INDIA, please contact:
"RED SOCIETY" at 9940217816. They will help the children for their studies.

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Everything is free. Contact : 045420-240668,245732
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-Plant more Trees.
-Don't waste Water & Electricity.
-Don't use or burn Plastics

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"TREES DO IT FOR FREE"
"Respect them and Save them"

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'Imitinef Mercilet' is a medicine which cures blood cancer. Its available free of cost at "Adyar Cancer Institute in Chennai". Create Awareness. It might help someone.
Cancer Institute in Adyar, Chennai
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Landmark: Near Michael School
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12. Please CHECK WASTAGE OF FOOD
If you have a function/party at your home in India and food gets wasted, don't hesitate to call 1098 (only in India ) - Its not a Joke, This is the number of Child helpline.
They will come and collect the food. Please circulate this message which can help feed many children.
AND LETS TRY TO HELP INDIA BE A BETTER PLACE TO LIVE IN
Please Save Our Mother Nature for
"OUR FUTURE GENERATIONS"
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Role model for everyone(worthful life )Live like a legend



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Generating Magic squares of odd order using De la loubre's Method



Enter the odd number it will generate a magic squares using De la Loubre's method. Magic squares is the matrix where row,column and diagonal sums are constant By
for e.g enter odd number say 9 then you will get the output as magic square as follows

and if you type 19 then

Read the method here
http://britton.disted.camosun.bc.ca/magicsq/magic.html
Download the code here
http://www.planet-source-code.com/vb/scripts/ShowCode.asp?txtCodeId=13423&lngWId=3
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Who is the Master?



Hello friends……….I thought of going for some psychological topics to discuss. To start with hmmm…………people believe that we all are slaves of something in the world. Some may be slave to bucks, power, food, sleep, war, pain, fear, emotions, feelings and love. It’s quite common to all living thing in the world to be salve to something/someone. Did you ever felt that you are slave of yourself; have to noticed that something within you ruling you, Strange things making you to do what you don’t. So how is the master in you and who’s slave are you.

Let’s take a simple example to explain things……….When you are asked to sit in a chair, which has a sharp nail tip waiting for you to prick you. Now you are forced to sit in it for some times so that you will win something precious to you. The moment you sit on the nail you will adjust yourself to have minimum pain caused by the prick. You will sit in a position so that you don’t fell much pain. Before you adjust yourself you will go in a series of positions to find the suitable position. Even after you got into a suitable position you won’t be comfortable in sitting in the chair. When the threshold of your resistance reaches you start to get away from the chair/ stand up. That’s it.

In this situation, it clearly explains that you have become slave not only to the precious thing but became slave to the master within you. So who is the master here? When you go deep in the series of action that you performed while sitting in the chair, we can have 2 competitors for the Master position- Brain and Body. The brain became master of the body when you are making yourself to do an action which your body doesn’t accept/resist. But the brain makes you to sit on the chair by controlling the body and became the master of you. As per the action continues, your brain lose its control of the body at a particular point where the body master the brain by having that the body has lost its resistance to the pain and it should be moved. The moment you find a suitable position with minimum pain, the body analyses the condition and after the threshold is reached, it takes over the brain and gains the position of the Masters of master (master of brain).

Now I wanna to put forth a question that “Who is your Master within you?” can we able to take hold of any of the master? Yes we can, but the master which will have some flexibility is the BRAIN. The body is a rigid master with no adjustment. You can practice your brain in such a way that it should feel that you are not in pain like oxyimoron Falling in love. This can be done practically by what the sadhu did to control the body. I want to make a little correction, make fool of the brain to master and intelligent body to serve.

“Try to control your body you will win things, but when you take hold your mind you can win your body”

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