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Dec
8
comment Why are integers subset of reals?
I think it's worth mentioning that real numbers in typical programming language are fixed-size, that roughly means fixed-precision, so they are very different from real numbers as defined in mathematics. Floating-point number types are an engineering artifact without any relation to clear and well-defined mathematical concept. Google "What Every Computer Scientist Should Know About Floating-Point Arithmetic" for the details.
Nov
19
comment Why do proof authors use natural language sentences to write proofs?
@pew yes I'm sorry about my wording. The point is, that at least for me, it's not obvious from the human language on that page that proving 2p - n > 0 is also necessary. No matter how trivial, without that assertion the whole argument breaks down.
Nov
19
comment Why do proof authors use natural language sentences to write proofs?
@pew: in your human-language proof, you forgot (iii) 2p - n > 0. If it's so easy to overlook in this trivial proof, more complex verbal proofs don't stand a chance :-)