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Math Help - Suppose that b<=L+e for all e>0. Prove b<=L

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    Suppose that b<=L+e for all e>0. Prove b<=L

    Suppose that b \leq L + \epsilon for all \epsilon > 0. Prove that b \leq L.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by qtpipi View Post
    Suppose that b \leq L + \epsilon for all \epsilon > 0. Prove that b \leq L.
    Suppose b>L then b-L=\delta>0, so let \varepsilon=\delta/2, then:

    b-L>\varepsilon>0

    or:

     <br />
b>L+\varepsilon<br />

    a contradiction.

    CB
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