> product of two compact spaces is compact > A strong opening! I looked it up and found Tychonoff's Theorem - looks interesting.
Beware! Those are not the same! The former is elementary, the latter is equivalent to the axiom of choice!
Because... that might... be really important. Someday. That you not mix those up. You know.
The diagonalization proof of the Halting Problem that someone mentioned up above is truly beautiful, much better than the classic diagonalization results *or* Goedel's first incompleteness theorem. I mostly put that generalized diagonalization theorem as my answer because it has some personal significance.
It might be fun to talk about favorite results, too. Of the top of my head, Stone-Weierstrass comes to mind (the proof is boring and technical, but the result is so neat! I hadn't thought of it in years but the Bolzano-Weierstrass stuff reminded me), or the curious embedding properties of the Cantor set. (That dude just keeps popping up...)
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timeasmymeasure
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Date: 2009-02-21 08:42 am (UTC)> A strong opening! I looked it up and found Tychonoff's Theorem - looks interesting.
Beware! Those are not the same! The former is elementary, the latter is equivalent to the axiom of choice!
Because... that might... be really important. Someday. That you not mix those up. You know.
The diagonalization proof of the Halting Problem that someone mentioned up above is truly beautiful, much better than the classic diagonalization results *or* Goedel's first incompleteness theorem. I mostly put that generalized diagonalization theorem as my answer because it has some personal significance.
It might be fun to talk about favorite results, too. Of the top of my head, Stone-Weierstrass comes to mind (the proof is boring and technical, but the result is so neat! I hadn't thought of it in years but the Bolzano-Weierstrass stuff reminded me), or the curious embedding properties of the Cantor set. (That dude just keeps popping up...)