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How many digits of π can you memorize?

#41

3.16 (it begins with "3", 1 digit, continues with ".", not really a digit but let's say one thenth of a digit for good measure, then continues with "1", the second digit, and then the next digit "4", now I run out of memory and with a chance of 6% I will guess the next digit right. Thus, I memorize 3 + 0.1 + 0.06 digits, if this makes any sense)

3.16 (it begins with "3", 1 digit, continues with ".", not really a digit but let's say one thenth of a digit for good measure, then continues with "1", the second digit, and then the next digit "4", now I run out of memory and with a chance of 6% I will guess the next digit right. Thus, I memorize 3 + 0.1 + 0.06 digits, if this makes any sense)
#42

@Mihir_katti said in #30:

Pi is infinite

Only time will tell...

@Mihir_katti said in #30: > Pi is infinite Only time will tell...
#43

@obladie said in #42:

Only time will tell...
Pi has infinitely many non-zero digits (which as I said above is not the same as being infinite). That has been proven. This is the strength of mathematics : you don't need to effectively compute digits of pi after digit of pi to know it will never end.

@obladie said in #42: > Only time will tell... Pi has infinitely many non-zero digits (which as I said above is not the same as being infinite). That has been proven. This is the strength of mathematics : you don't need to effectively compute digits of pi after digit of pi to know it will never end.
#44

@polylogarithmique said in #43:

Pi has infinitely many non-zero digits (which as I said above is not the same as being infinite). That has been proven. This is the strength of mathematics : you don't need to effectively compute digits of pi after digit of pi to know it will never end.

You are wrong. It's not proven. Actually Pi is limited but sadly even supercomputers can't find last digit of Pi just like quantum computers can't solve chess.
Someday both things will be solved.

@polylogarithmique said in #43: > Pi has infinitely many non-zero digits (which as I said above is not the same as being infinite). That has been proven. This is the strength of mathematics : you don't need to effectively compute digits of pi after digit of pi to know it will never end. You are wrong. It's not proven. Actually Pi is limited but sadly even supercomputers can't find last digit of Pi just like quantum computers can't solve chess. Someday both things will be solved.
#45

@Akbar2thegreat pi is proven to be transcendental, in particular it is irrational, in particular it has infinitely many non-zero digits.

https://www.grc.nasa.gov/www/k-12/Numbers/Math/Mathematical_Thinking/transcendentality_of_p.htm

https://en.m.wikipedia.org/wiki/Transcendental_number

https://someclassicalmaths.wordpress.com/2009/11/21/pi-is-transcendental/

@Akbar2thegreat pi is proven to be transcendental, in particular it is irrational, in particular it has infinitely many non-zero digits. https://www.grc.nasa.gov/www/k-12/Numbers/Math/Mathematical_Thinking/transcendentality_of_p.htm https://en.m.wikipedia.org/wiki/Transcendental_number https://someclassicalmaths.wordpress.com/2009/11/21/pi-is-transcendental/
#46

@polylogarithmique
Pi is transcendental number and I know that but it doesn't have unlimited digits and there's no proof for the same.
It has last digit in existence waiting to be discovered by quantum computers.

@polylogarithmique Pi is transcendental number and I know that but it doesn't have unlimited digits and there's no proof for the same. It has last digit in existence waiting to be discovered by quantum computers.
#47

@Akbar2thegreat if pi has a finite number of digits, it means pi=n/10^k for some positive integers n and k.
But then pi is a solution of the equation (10^k)x-n=0, contradicting the fact that it is a transcendental number.

@Akbar2thegreat if pi has a finite number of digits, it means pi=n/10^k for some positive integers n and k. But then pi is a solution of the equation (10^k)x-n=0, contradicting the fact that it is a transcendental number.
#48

@polylogarithmique
That's not enough to say that last digit of Pi doesn't exist.
Don't you know that transcendental numbers can be solution to equations in mathematics?

@polylogarithmique That's not enough to say that last digit of Pi doesn't exist. Don't you know that transcendental numbers can be solution to equations in mathematics?
#49

It's amusing that you downvote a quite elementary mathematical argument.

It's amusing that you downvote a quite elementary mathematical argument.
#50

@Akbar2thegreat said in #48:

@polylogarithmique
That's not enough to say that last digit of Pi doesn't exist.
It is.
Don't you know that transcendental numbers can be solution to equations in mathematics?
I know. However the equation I wrote is not any equation. It is a polynomial equation (of degree 1) with non-zero integer coefficient. By definition transcendental means pi is not the solution of ANY polynomial equation with non-zero integer coefficient. In particular it is not a solution of the equation I wrote.

@Akbar2thegreat said in #48: > @polylogarithmique > That's not enough to say that last digit of Pi doesn't exist. It is. > Don't you know that transcendental numbers can be solution to equations in mathematics? I know. However the equation I wrote is not any equation. It is a polynomial equation (of degree 1) with non-zero integer coefficient. By definition transcendental means pi is not the solution of ANY polynomial equation with non-zero integer coefficient. In particular it is not a solution of the equation I wrote.

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