Explain why the interval $|y-1|<B$ cannot contain $y=0$ only when $0<B<1$.
I'm not sure where $0<B<1$ comes from
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It doesn't "come from" anywhere. It's the hypothesis for what you are asked to prove. Try by contradiction: what if $B$ is not in that interval? PS You've asked other questions here that have been answered. You should accept answers that help you (the check box) and upvote them too (the up arrow). – Ethan Bolker Feb 12 '17 at 14:55
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It's not quite true.
If $B \le 0$, the "interval" is empty, so we wouldn't call it an interval.
If $B > 1$. the interval does contain $0$, because $|0-1| = 1$.
But the interval doesn't contain $0$ when $B=1$.
Robert Israel
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Thank you. I understand where this is coming from now. But how would we know what values of B to look at if we were NOT given the interval $0<B<1$? – thebuddha Feb 12 '17 at 15:08
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With $0\leq|y-1|<B$ we know $0<B$ and when $|y-1|<B$ then $$1-B<y<1+B$$ but this can't contain $y=0$ so $0<1-B<y$ which concludes $\color{blue}{0<B<1}$.
Nosrati
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