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There is also this: http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis It uses intuitionist
by nova 17y ago
There is also this:
http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis
It uses intuitionistic logic, so no axiom of choice.
- btilly 17y agoNo axiom of choice, but most working mathematicians reject constructivism. Plus there are some pretty big differences. Do you really want to explain to students why you don't consider f(x) = 1 if x >= 1 and 0 otherwise to be a valid definition of a function? And (in some ways more importantly) why most of the rest of the world does? Furthermore the intermediate value theorem is pretty useful and I wouldn't want to lose it.
- nova 17y agoJust mentioning another approach. I don't really understand it myself, but I kind of find it intriguing because of its relation to computability aspects.