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Proving the well ordering principle starting from the axiom of completeness. Is this topological proof valid?
While reading this SE thread, I saw in the comments someone say "the proof [that the completeness axiom implies the well ordering principle] will take some work".
However, this other thread ...
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Is it legal to define a function that gives different results for 1.0 and for 1?
In programming languages I can define such function, because in most programming languages 1.0 is not 1, because 1.0 has type "float", and 1 has type "integer". In math I don't see ...
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