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[4th year undergrad mathematics] please explain rigorously the difference between continuity and UNIFORM continuity to me.
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We were talking about it today in class, and my professor wrote down this as the definition for uniform continuity of a function f: R-->R
for all e>0, there exists d>0 so that if |x-y|<d, then |f(x) -f(y)|<e.
x,y in R.
This looks EXACTLY like regular continuity to me.
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