Real Analysis question about uniform continuity. I know that a constant function is uniformly continuous.
We have a function f: [0,+inf] - > R
Say f(x) = 1 for x in [0,1] and f(x) = 2 for x in [1,+inf)
Is f uniformly continuous on [0,+inf) ?
I think that if instead f(x) = 1 for x in [0,1) (not including 1) and f(x) = 2 for x in [1,+inf), then it would not be continuous at 1 so it cannot be uniformly continuous on [0,+inf). But since it's [0,1] and [1,+inf), I'm not sure if it is or is not.
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