Why do we call the Urysohn lemma a “deep” theorem? Because its proof involvesĪ really original idea, which the previous proofs did not. Here is Munkres introducing a hard theorem in chapter 4 of 'Topology' The three theorems are (1) the intermediate value theorem, and a continuous function on a closed interval is (2) bounded and (3) achieves its supremum. In this context "hard" means making essential use of the completeness property not nearly as hard as the prime number theorem but a major step up in sophistication for the intended reader. TeX all the things Chrome extension (configure inline math to use delimiters) MathJax userscript (userscripts need Greasemonkey, Tampermonkey or similar) To view LaTeX on reddit, install one of the following: If you feel you were banned unjustly, or that the circumstances of your ban no longer apply, see our ban appeal process here.Ĭareer and Education Questions - every ThursdayĪ Compilation of Free, Online Math Resources. If you post or comment something breaking the rules, the content may be removed - repeated removal violations may escalate to a ban, but not without some kind of prior warning see here for our policy on warnings and bans. This subreddit is actively moderated to maintain the standards outlined above as such, posts and comments are often removed and redirected to a more appropriate location. Unnecessarily combative or unkind comments may result in an immediate ban. racism, sexism, homophobia, hate speech, etc.). This includes not only comments directed at users of /r/math, but at any person or group of people (e.g. If you upload an image or video, you must explain why it is relevant by posting a comment providing additional information that prompts discussion.ĭo not troll, insult, antagonize, or otherwise harass. Memes and similar content are not permitted. Image/Video posts should be on-topic and should promote discussion. If you are asking for advice on choosing classes or career prospects, please post in the stickied Career
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