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**I-Think** There are 2 ways of saying a function,$\displaystyle f$, is uniformly continuous

A. For every $\displaystyle \epsilon>0$, there exists a $\displaystyle \delta>0$ such that

$\displaystyle |f(x)-f(p)|<\epsilon$ whenever $\displaystyle x,p\in{I}$ and $\displaystyle |x-p|<\delta$

B. For every $\displaystyle \epsilon>0$, there exists a $\displaystyle \delta>0$ such that

$\displaystyle |f(x)-f(p)|\leq\epsilon$ whenever $\displaystyle x,p\in{I}$ and $\displaystyle |x-p|\leq\delta$

Prove f satisfies A if and only if it satisfies B

This is a confusing proposition. I think if f satisfies B, then it obviously satisfies A, but I could be mistaken.

And if it satisfies A, how do I go about demonstrating B?

Thanks in advance for the help