ProofWiki

Time 2020-09-27 20:04:49

Web Name: ProofWiki

WebSite: http://proofwiki.org

ID:62047

Keywords:

ProofWiki,

Description:

ProofWiki is an online compendium of mathematical proofs! Our goal is the collection, collaboration and classification of mathematical proofs. If you are interested in helping create an online resource for math proofs feel free to register for an account. Thanks and enjoy!If you have any questions, comments, or suggestions please post on the discussion page, or contact one of the administrators. Also, feel free to take a look at the frequently asked questions because you may not be the first with your idea.To see what's currently happening in the community, visit the community portal.20,525 Proofs — 16,205 Definitions — HelpFollow @ProofWikiFeatured ProofReal Plus EpsilonTheoremLet $a, b \in \R$, such that:$\forall \epsilon \in \R_{ 0}: a b + \epsilon$where $\R_{ 0}$ is the set of strictly positive real numbers.That is:$\epsilon 0$Then:$a \le b$ProofAiming for a contradiction, suppose $a b$.Then:$a - b 0$By hypothesis, we have:$\forall \epsilon 0: a b + \epsilon$Let $\epsilon = a - b$.Then:$a b + \paren {a - b} \implies a a$The result follows by Proof by Contradiction.$\blacksquare$Sources1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 1$: Real Numbers: $\S 1.7$: Example This page was last modified on 16 March 2018, at 01:00 and is 874 bytesContent is available under Creative Commons Attribution-ShareAlike License unless otherwise noted.

TAGS:ProofWiki 

<<< Thank you for your visit >>>

Hot Websites