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Mathematics for computersThu, 21 Jul 2016 20:45:57 +0000hourly1https://wordpress.org/?v=4.6-alpha-37362Comment on Proof of negation and proof by contradiction by Andrej Bauer
http://math.andrej.com/2010/03/29/proof-of-negation-and-proof-by-contradiction/comment-page-1/#comment-66192
Thu, 21 Jul 2016 20:45:57 +0000http://math.andrej.com/?p=453#comment-66192@Arik: well, if you’re their teacher perhaps you can teach them about the distinction.
]]>Comment on Constructive gem: an injection from Baire space to natural numbers by What is an injection in a topos? - mathfreebook
http://math.andrej.com/2011/06/15/constructive-gem-an-injection-from-baire-space-to-natural-numbers/comment-page-1/#comment-66183
Wed, 20 Jul 2016 22:34:41 +0000http://math.andrej.com/?p=968#comment-66183[…] Space $mathbb{N}^mathbb{N}$ to the natural numbers $mathbb{N}$. This is discussed in Andrej’s blog […]
]]>Comment on Proof of negation and proof by contradiction by Arik
http://math.andrej.com/2010/03/29/proof-of-negation-and-proof-by-contradiction/comment-page-1/#comment-66051
Fri, 15 Jul 2016 15:24:30 +0000http://math.andrej.com/?p=453#comment-66051I encounter the following problem: students call proof by negation (meaning reduction to contradiction) when in order to prove “if p then q” they prove that “if not q then not p”. The latter uses clearly the tautology that ” ‘if p then q’ iff ‘if not q then not p’ “. This type of proof is called contrapositive but students are not aware to the distinction.
]]>Comment on The real numbers in homotopy type theory (CCA 2016 slides) by Andrej Bauer
http://math.andrej.com/2016/06/15/the-real-numbers-in-homotopy-type-theory-cca-2016-slides/comment-page-1/#comment-65757
Sat, 25 Jun 2016 11:16:32 +0000http://math.andrej.com/?p=1898#comment-65757@Cale: If we leave out the set truncation then we will get the freely generated higher-path structure, whatever that is, because we have an inductive definition. I have not thought whether this structure could be interesting, I always presumed it is not. But who knows!
]]>Comment on The real numbers in homotopy type theory (CCA 2016 slides) by Max New
http://math.andrej.com/2016/06/15/the-real-numbers-in-homotopy-type-theory-cca-2016-slides/comment-page-1/#comment-65749
Fri, 24 Jun 2016 16:35:44 +0000http://math.andrej.com/?p=1898#comment-65749I was also interested in the Sierpinski space construction he mentioned, and I found it on the TYPES website here: http://www.types2016.uns.ac.rs/images/abstracts/altenkirch2.pdf
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