How many digits of π can you memorize?

@obladie said in #61:

Actually, you do. No repeat has yet been arrived at, and the best math indicates there will never be one.
It doesn't 'indicate'. It proves. Because a number whose digits keep repeating themselves is a rational number (easy exercise), and it has been proved pi is irrational.

@Akbar2thegreat said in #58:

You don't even know basic logic
I do actually. I a mathematician by formation, and I studied in particular formal logic and mathematical logic.

You didn't "break science". You're just too infatuated with yourself to see that what you're saying is utter garbage.

@polylogarithmique said in #62:

It doesn't 'indicate'. It proves. Because a number whose digits keep repeating themselves is a rational number (easy exercise), and it has been proved pi is irrational.

Proof requires an infinite number of experiments all exactly the same all giving the same result. Real scientists never say something is "proved".

@obladie what you are saying applies to experimental sciences.

The concept of proof in mathematics is very different. It solely relies on unfolding logical consequences from our assumptions (sometimes known as axioms).

For instance, you don't need an infinite number of experiments to know that the sum of two odd numbers will always be even. You just need the few lines below:

Let n and m be odd integers.
By definition of odd, this means there exist integers k and l such that n=2k+1 and m=2l+1.
Hence n+m=(2k+1)+(2l+1).
By associativity and commutativity of addiction, we get that n+m=2k+2l+2.
By distributivity of multiplication over addition, this becomes n+m=2(k+l+1).
The sum of three integers ks still an integer, hence we wrote n+m as the double of an integer.
By definition of even, this means that n+m is even.

@polylogarithmique said in #65:

@obladie what you are saying applies to experimental sciences.

The concept of proof in mathematics is very different. It solely relies on unfolding logical consequences from our assumptions (sometimes known as axioms).

No it isn't. I am really old, and only hold a low level math degree, but I still know you are wrong.

You also don't need to look at infinitely many rectangle triangles to know that Pythagoras theorem holds. Instead you only need the few lines below:

Let T be a rectangle triangles whose perpendicular sides are given by two orthogonal vectors u and v.
Then the hypothenuse is given by the vector u-v.
So the square lenght of the hypothenuse is ||u-v||^2=[u-v,u-v], where [-, -] denotes the inner product.
By bilinearity of the inner product, this is ||u-v||^2=||u||^2+||v||^2-[u,v]-[v,u].
But the fact that u and v are orthogonal means [u, v] =[v, u] =0, hence we arrive at ||u-v||^2=||u||^2+||v||^2, that is, the square of the lenght of the hypothenuse equals the sum of the squares of the other two side lenghts.

@obladie said in #67:

No it isn't. I am really old, and only hold a low level math degree, but I still know you are wrong.
Well I hold a high level low degree, and I know I am right :)

You do not hold any math qualifications. Goodbye.
My other degrees are Chemistry and another low level Physics degree.
And one lonely non-science one.

You can read more about it there https://en.m.wikipedia.org/wiki/Mathematical_proof
https://en.m.wikipedia.org/wiki/Formal_proof
or if you prefer dealing directly with the words of some professional mathematicians
https://math.berkeley.edu/~hutching/teach/proofs.pdf
https://webspace.maths.qmul.ac.uk/a.shao/intro/begin/proof.php
https://profkeithdevlin.org/2014/11/24/what-is-a-proof-really/