Interesting mathematical statements (1 Viewer)

Paradoxica

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I know lol. This is one of the biggest mind gobbling problems to pure mathematicians apparently; WHY?
The thing is, we don't even know how to begin to approach this problem. Paul Erdos has already commented on this problem.
Looks like we'll just have to wait for the next
Euler/Erdos/Tao/Gauss/Noether/Polya/Hilbert/Russell/Lagrange/Riemann/Hardy/Poincare/Fermat/Grothendieck/Newton/Leibniz/Weierstrass/Cauchy/Descartes/Dirichlet/Cantor/Fibonacci/Jacobi/Ramanujan/Hamilton/Godel/Pascal/Apollonius/Laplace/Liouville/Eisenstein/Banach/Peano/Bernoulli/Viete/Fourier/Huygens/Chebyshev/Lebesgue/Turing/Cardano/Minkowski/Littlewood/Legendre/Birkhoff/Lambert/Poisson/Wallis/Tarski/Frege/Hausdorff/Neumann/Galois
to come around and resolve the problem.

 

glittergal96

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If you have a small ball in 3 dimensional space, it is possible to decompose it as a union of a finite number of sets, which can be moved by rotations and translations such that the pieces never overlap and such that the final object constructed is an arbitrarily large ball.

Colloquially, one can cut a pea into a finite number of pieces and reassemble it into something the size of the sun.
 

leehuan

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Can we keep our posts restrained to at least MX2 level and not making bad usages of mathematics lmao
 

KingOfActing

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Zeta regularisations are important

1 + 2 + 3 + ... =/= -1/12, but is rather 'assigned' that value
 

InteGrand

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I like the 1 + 2 + 3 + 4 + … = -1/12 result, and find it also quite amazing that this is used in physics and gives some experimentally verifiable results. There's a lot of 'weird' stuff like this in this series of lectures on Mathematical Physics by Carl Bender that can be found on YouTube.

Also, I think this thread should be in the maths Extracurricular Topics forum.
 

Paradoxica

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If you have a small ball in 3 dimensional space, it is possible to decompose it as a union of a finite number of sets, which can be moved by rotations and translations such that the pieces never overlap and such that the final object constructed is an arbitrarily large ball.

Colloquially, one can cut a pea into a finite number of pieces and reassemble it into something the size of the sun.
Only if I accept the axiom of choice. : PPPPPPP
 

glittergal96

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Only if I accept the axiom of choice. : PPPPPPP
Even if you don't accept the axiom of choice (which is a bit limiting, but some minority of mathematicians don't), you would not be able to prove that such a reassembling of the pea into the sun is impossible. (Because the axiom of choice is consistent with the other axioms of set theory.)

This is still pretty unintuitive.
 

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