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Is an equivalence relation (= sign) needed for the real number system or is a consequence of the other axioms?
My math education is based on Calculus or Real Analysis didactical books intended for bachelor's degrees, mainly read in chunks, and never went any further.
Generally, the Real Number System is said ...
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10
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Foundation of ordering of real numbers
This might be a silly question, but what is the mathematical foundation for the ordering of the real numbers? How do we know that $1<2$ or $300<1000$... Are the real numbers simply defined as ...
user116403
4
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How do we decide which axioms are necessary?
I am studying the axioms for a complete ordered field. I have looked at different sources, some of which differ slightly in their listings.
Given some construction of the reals (e.g. Dedekind cuts or ...
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