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Mathematics for computersMon, 19 Dec 2016 22:07:51 +0000hourly1https://wordpress.org/?v=4.7-alpha-38868Comment on Five stages of accepting constructive mathematics by Andrej Bauer
http://math.andrej.com/2016/10/10/five-stages-of-accepting-constructive-mathematics/comment-page-1/#comment-71990
Mon, 19 Dec 2016 22:07:51 +0000http://math.andrej.com/?p=1962#comment-71990Then you cannot do any serious mathematics, as I explained in this MathOverflow answer.
]]>Comment on Random Art and the Law of Rotten Software by Benjamin Weaver
http://math.andrej.com/2010/08/17/random-art-and-the-law-of-rotten-software/comment-page-1/#comment-71921
Mon, 19 Dec 2016 03:06:02 +0000http://math.andrej.com/?p=541#comment-71921Well, it looks like it’s been over three years since anyone commented. I’ll just say that I love the Random Art generator/page/software, whatever you want to call it. I’m glad the page is still up. It has been invaluable to me. Thanks!
]]>Comment on Five stages of accepting constructive mathematics by Ron
http://math.andrej.com/2016/10/10/five-stages-of-accepting-constructive-mathematics/comment-page-1/#comment-71848
Sat, 17 Dec 2016 20:12:22 +0000http://math.andrej.com/?p=1962#comment-71848… And what if I change selection/specification so that a subset cannot be defined by an arbitrary predicate but only by a decidable one?
]]>Comment on Five stages of accepting constructive mathematics by Ron
http://math.andrej.com/2016/10/10/five-stages-of-accepting-constructive-mathematics/comment-page-1/#comment-71847
Sat, 17 Dec 2016 20:03:33 +0000http://math.andrej.com/?p=1962#comment-71847Oh, and I guess that an axiom stating that all subsets of finite sets are decidable (and therefore finite) would yield choice for finite sets which would enough to get LEM, right?
]]>Comment on Five stages of accepting constructive mathematics by Andrej Bauer
http://math.andrej.com/2016/10/10/five-stages-of-accepting-constructive-mathematics/comment-page-1/#comment-71846
Sat, 17 Dec 2016 19:42:45 +0000http://math.andrej.com/?p=1962#comment-71846The subsets are not presumed to be decidable. And you can’t just say things like “what if I represent the subset input as a computation from {0,1} -> {TRUE, FALSE} and test if 0 and/or 1 are present in the subset” without first properly setting up an interpretation of logic and set theory (or whatever formalism you have in mind) under which it is even possible to represent subsets as computations. You would probably need to use something like realizaiblity. However, note that general subsets cannot be represented by binary functions because not all subsets are decidable. Regarding your third option: that is just describing countable sets, possibly with decidable equality. And as soon as you say “realized” that means you’re at stage three and you’re thinking of a particular model. Whatever you discover a particular model may not be applicable to constructive mathematics in general.
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