Re: functions of uncountably many variables
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so the function g(x)=x+1 is actually a function of infinately many variables, not one? lame.
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Not really. But you could say that g(f(x))=f(x)+1 is a function of infinitely many variables.
Functions that operate on real functions rather than operating on real numbers are effectively functions of uncountably many variables.
I don't know that you'd ever want to do it but the characteristic function of continuity g:f->{0,1} which is 1 if f is continuous everywhere, and 0 otherwise.
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