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

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

Suppose that $b \leq$ $L + \epsilon$ for all $\epsilon > 0$. Prove that $b \leq L$.

2. Originally Posted by qtpipi
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:

$
b>L+\varepsilon
$