Feb. 19th, 2009

ciphergoth: (Default)
Some really interesting answers on what proofs you know. The most common proofs people mention are the ones I name, plus Cantor's diagonalisation argument that |R| > |N| - cool. More specific comments follow.
[livejournal.com profile] wildbadger -- product of two compact spaces is compact
A strong opening! I looked it up and found Tychonoff's Theorem - looks interesting.
[livejournal.com profile] cryptodragon -- A number of them from crypto stuff
Interesting, name us a favourite?
[livejournal.com profile] simple_epiphany -- As a third-year maths student, I'm required to know quite a lot of them, but the one for the Bolzano-Weierstrass theorem is quite nice.
Bolzano–Weierstrass theorem on Wikipedia. I think I could remember that proof. Cool, thanks!
[livejournal.com profile] aegidian -- Cantor's Diagonalisation, proving there are as many rational numbers as there are integers.
Ah, the proof that |Q| = |N| rather than the proof that |R| > |N|?
[livejournal.com profile] olethros -- Maybe I lied. I can prove (by recursion) that all marbles in the world are the same colour.
I know that proof :-) Oh go on, there must be a *valid* proof you like!
[livejournal.com profile] keirf -- Bolzano-Weierstrass theorem - every bounded sequence in R{n} has a convergent subsequence
A second showing for this theorem!
[livejournal.com profile] ajva -- that 0.999...=1
Don't you need to get into the construction of the real numbers to explain this one?
[livejournal.com profile] ergotia -- The infinite number of primes/hotel at the end of the universe one
Two proofs for the price of one :-)
[livejournal.com profile] nikolasco -- irrationality of sqrt(2) (fundamental theorem of arithmetic, even/odd, well-ordered)
What proofs are you referring to with "even/odd, well-ordered"?
Thanks all, please keep commenting :-)

Profile

ciphergoth: (Default)
Paul Crowley

January 2025

S M T W T F S
   1234
5678 91011
12131415161718
19202122232425
262728293031 

Most Popular Tags

Page Summary

Style Credit

Expand Cut Tags

No cut tags
Page generated Sep. 25th, 2025 05:33 pm
Powered by Dreamwidth Studios