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How many digits of π can you memorize?

#51

@polylogarithmique
Actually there are few terms in maths which are wrongly defined.
One of them being about transcendental number.
I can propose changes but they will have to be universally accepted.

@polylogarithmique Actually there are few terms in maths which are wrongly defined. One of them being about transcendental number. I can propose changes but they will have to be universally accepted.
#52

You can change the definition as much as you want, it won't change the fact that pi is provably not a solution of any non-zero polynomial equation with integer coefficients. In particular, it won't change the fact that pi is not the ratio of two integers, and hence has infinitely many non-zero digits.

And by the way there is no such thing as a "wrongly defined" term in maths. In maths, a definition is just an abbreviation, AND NOTHING MORE: it is shorter to write "transcendantal" than "not a solution of any non-zero polynomial equation with integer coefficient".
But then when you go on to prove that pi is transcendental, what you are proving is the statement of which "transcendental" is the abbreviation. Namely, that pi is not a solution of any non-zero polynomial equation with integer coefficient.
The choice of what terms are used is completely arbitrary, and is not related to their usual meaning outside the realms of mathematics. We could as well have decided to abbreviate "not a solution of any non-zero polynomial equation with integer coefficient" by "cowardly" or "blue" or even "bulbbogly" and then Lindemann's proof would imply that pi is cowardly or blue or bulbbogly. For historical reasons, people chose the term "transcendental", but it has no meaning other than being the abbreviation of "not a solution of any non-zero polynomial equation with integer coefficient".
In particular it has nothing (but REALLY NOTHING) to do with the concepts of "transcendental" that are related to philosophy or religion.

You can change the definition as much as you want, it won't change the fact that pi is provably not a solution of any non-zero polynomial equation with integer coefficients. In particular, it won't change the fact that pi is not the ratio of two integers, and hence has infinitely many non-zero digits. And by the way there is no such thing as a "wrongly defined" term in maths. In maths, a definition is just an abbreviation, AND NOTHING MORE: it is shorter to write "transcendantal" than "not a solution of any non-zero polynomial equation with integer coefficient". But then when you go on to prove that pi is transcendental, what you are proving is the statement of which "transcendental" is the abbreviation. Namely, that pi is not a solution of any non-zero polynomial equation with integer coefficient. The choice of what terms are used is completely arbitrary, and is not related to their usual meaning outside the realms of mathematics. We could as well have decided to abbreviate "not a solution of any non-zero polynomial equation with integer coefficient" by "cowardly" or "blue" or even "bulbbogly" and then Lindemann's proof would imply that pi is cowardly or blue or bulbbogly. For historical reasons, people chose the term "transcendental", but it has no meaning other than being the abbreviation of "not a solution of any non-zero polynomial equation with integer coefficient". In particular it has nothing (but REALLY NOTHING) to do with the concepts of "transcendental" that are related to philosophy or religion.
#53

I guess @ MrPushwood was right when he said this would be a geek detection system...

I guess @ MrPushwood was right when he said this would be a geek detection system...
#55

@polylogarithmique
By 'definition' I meant that ratio should have been categorised more as normal ratio p/q (where p and q are some integers) and proper ratio, where denominator is not of form 10^n for some integer n.
Hence, my definition for transcendental:
'Number that cannot be of form p/q where q=10^n for integers p, q and n'
So, according to my definition,
Pi is not transcendental.
According to my definition,
Last digit of Pi exists.
Q.E.D.
Also, there is a proven method to find last digit of various type of numbers in mathematics. And it doesn't say that it doesn't apply to transcendental numbers.
Using that method, it shows that last digit of Pi comes out to be 3 but since the memory is not enough it can't call all digits. Supercomputers will take time to call all the digits if they accept my definition.

@polylogarithmique By 'definition' I meant that ratio should have been categorised more as normal ratio p/q (where p and q are some integers) and proper ratio, where denominator is not of form 10^n for some integer n. Hence, my definition for transcendental: 'Number that cannot be of form p/q where q=10^n for integers p, q and n' So, according to my definition, Pi is not transcendental. According to my definition, Last digit of Pi exists. Q.E.D. Also, there is a proven method to find last digit of various type of numbers in mathematics. And it doesn't say that it doesn't apply to transcendental numbers. Using that method, it shows that last digit of Pi comes out to be 3 but since the memory is not enough it can't call all digits. Supercomputers will take time to call all the digits if they accept my definition.
#56

@Akbar2thegreat you are clearly not even understanding what you are talking about.

A number that has finitely many digits after the decimal point can ALWAYS be written as n/10^k for some non-zero integers n and k. For instance 2.5=25/10, 7.11=711/100, 8.698546=8698546/1000000, I hope you see the pattern.

According to your definition pi IS transcendental. It HAS BEEN PROVEN (also there is already a term for your "definition", namely "not a decimal fraction").

And more importantly, facts do not depend on definitions. Definitions are just semantics. THE FACT THAT PI HAS INFINITELY MANY NON-ZERO DIGITS HAS BEEN MATHEMATICALLY PROVED. By changing the definition of 'transcendental' you're not going to change this fact.

It's like saying if I re-define 'tank' to be any military vehicle, there is no more war in Ukraine. You can do whatever you want with the WORDS, it does not change the state of the WORLD.

Also, there is a proven method to find last digit of various type of numbers in mathematics. And it doesn't say that it doesn't apply to transcendental numbers.
I have no idea what "it" is (in "it doesn't say") but transcendental numbers are in particular irrational, and irrational numbers have infinitely many digits. It's completely classical and straightforward, a first year maths student could prove it (and I kind of did in my previous posts).

You are trying to go against well-established facts, anyone who knows a bit about mathematics knows you're completely wrong. At this point your claims are as baseless as those people who claim the Earth is flat or that Australia doesn't exist. All you're doing is spreading some misinformation that could mislead some naive people.

@Akbar2thegreat you are clearly not even understanding what you are talking about. A number that has finitely many digits after the decimal point can ALWAYS be written as n/10^k for some non-zero integers n and k. For instance 2.5=25/10, 7.11=711/100, 8.698546=8698546/1000000, I hope you see the pattern. According to your definition pi IS transcendental. It HAS BEEN PROVEN (also there is already a term for your "definition", namely "not a decimal fraction"). And more importantly, facts do not depend on definitions. Definitions are just semantics. THE FACT THAT PI HAS INFINITELY MANY NON-ZERO DIGITS HAS BEEN MATHEMATICALLY PROVED. By changing the definition of 'transcendental' you're not going to change this fact. It's like saying if I re-define 'tank' to be any military vehicle, there is no more war in Ukraine. You can do whatever you want with the WORDS, it does not change the state of the WORLD. > Also, there is a proven method to find last digit of various type of numbers in mathematics. And it doesn't say that it doesn't apply to transcendental numbers. I have no idea what "it" is (in "it doesn't say") but transcendental numbers are in particular irrational, and irrational numbers have infinitely many digits. It's completely classical and straightforward, a first year maths student could prove it (and I kind of did in my previous posts). You are trying to go against well-established facts, anyone who knows a bit about mathematics knows you're completely wrong. At this point your claims are as baseless as those people who claim the Earth is flat or that Australia doesn't exist. All you're doing is spreading some misinformation that could mislead some naive people.
#57

the way you added qed at the end like that was a definitive proof genuinely got me lol

the way you added qed at the end like that was a definitive proof genuinely got me lol
#58

@polylogarithmique
I have already made changes to some debatable terms/rule in fields of science, maths and chess.
And all these (not mentioned as it would take up entire space and down Lichess) are 'my' proposed rules.
Changing definition changes meaning and changes way of interpretation and usage.
You don't even know basic logic and I know that Pi is transcendental according to universal rules but see those things from your eyes and not from axioms made already.
Use your own brain and think logically.
You will also find some terms ambiguous when you pay attention to them.
'Changes have to be made over time'
This applies in all fields.
Hence, I was just proposing my system of how something can be changed just like I have previously said on threads here by changing some chess rules and science ones as well.
Hope you get what I meant!

@CalbernandHowbe
Lol! It's my style to say QED often in debates with someone. Also, see above words where I finally broke silence over what I have been talking about Pi being transcendental.

@polylogarithmique I have already made changes to some debatable terms/rule in fields of science, maths and chess. And all these (not mentioned as it would take up entire space and down Lichess) are 'my' proposed rules. Changing definition changes meaning and changes way of interpretation and usage. You don't even know basic logic and I know that Pi is transcendental according to universal rules but see those things from your eyes and not from axioms made already. Use your own brain and think logically. You will also find some terms ambiguous when you pay attention to them. 'Changes have to be made over time' This applies in all fields. Hence, I was just proposing my system of how something can be changed just like I have previously said on threads here by changing some chess rules and science ones as well. Hope you get what I meant! @CalbernandHowbe Lol! It's my style to say QED often in debates with someone. Also, see above words where I finally broke silence over what I have been talking about Pi being transcendental.
#59

@Akbar2thegreat
For my purposes of this proof, I define the term “integer” to be any number not divisible by 1
Hence pi is an integer
Hence it is not irrational or transcendental as no integers are irrational or transcendental
Q.E.D.

Changes have to be made over time. I am sure my revolutionary new definition is extremely sensible and will definitely be accepted soon by mathematicians around the world

@Akbar2thegreat For my purposes of this proof, I define the term “integer” to be any number not divisible by 1 Hence pi is an integer Hence it is not irrational or transcendental as no integers are irrational or transcendental Q.E.D. Changes have to be made over time. I am sure my revolutionary new definition is extremely sensible and will definitely be accepted soon by mathematicians around the world
#60

besides lol even if your new definition for transcendence was accepted then pi would still be transcendental as unfortunately you’re just wrong about there being a last digit :D it goes on forever and ever, literally just google it, unless you’re saying it’s all a conspiracy

besides lol even if your new definition for transcendence was accepted then pi would still be transcendental as unfortunately you’re just wrong about there being a last digit :D it goes on forever and ever, literally just google it, unless you’re saying it’s all a conspiracy
#61

@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.

Actually, you do. No repeat has yet been arrived at, and the best math indicates there will never be one.

@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. Actually, you do. No repeat has yet been arrived at, and the best math indicates there will never be one.

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