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real analysis problem
a function f: R -> R has the property that for any four real numbers a, b, c, d such that a - b > c - d, we have f(a) - f(b) > f(c) - f(d). prove that f is a linear function, ie f(x) = mx + n for all x belonging to R, where m, n belong to R and m > 0
Re: real analysis problem
Are you supposed to prove that f can be a linear function, or f has to be a linear function?
Last edited by Ricky (2006-03-15 02:28:26)
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."