Suppose that $\displaystyle b \leq$ $\displaystyle L + \epsilon$ for all $\displaystyle \epsilon > 0$. Prove that $\displaystyle b \leq L$.
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Originally Posted by qtpipi Suppose that $\displaystyle b \leq$ $\displaystyle L + \epsilon$ for all $\displaystyle \epsilon > 0$. Prove that $\displaystyle b \leq L$. Suppose $\displaystyle b>L$ then $\displaystyle b-L=\delta>0$, so let $\displaystyle \varepsilon=\delta/2$, then: $\displaystyle b-L>\varepsilon>0$ or: $\displaystyle b>L+\varepsilon $ a contradiction. CB
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