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Math Help - Continuity proof

  1. #1
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    Continuity proof

    Question

    Show that every function f: \mathbb{Z} \to \mathbb{R} is continuous.


    Any ideas?

    Thanks.
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  2. #2
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    Quote Originally Posted by WWTL@WHL View Post
    Question

    Show that every function f: \mathbb{Z} \to \mathbb{R} is continuous.


    Any ideas?

    Thanks.
    For every \epsilon > 0 let \delta = \tfrac{1}{2} then the \delta-neighorhood of n\in \mathbb{Z} contains only itself in \mathbb{Z}.
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  3. #3
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    And done.

    Excellent. Thank you, PH.
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