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Math Help - Uniform Continuity Proof

  1. #1
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    Uniform Continuity Proof

    Prove that f is uniformly continuous on [1,2] by assuming the fact that f is continuous on (0,inf).

    Since f is continuous (0, inf) then f is continuous on [1,2]. Then by theorem, If f is continuous on a closed interval [1,2], then f is unifromly continuous on [1,2].

    I was just wondering how I can justify that if f is continuous on (0, inf) then f is continuous on [1,2]. It seems obvious just I don't know how it should be formally. Like a restriction of a continuous function is continuous.

    Thanks
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  2. #2
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    Because \left[ {1,2} \right] \subset \left( {0,\infty } \right) then if x \in \left[ {1,2} \right], f is continous at x by the given.
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