Explain why the interval $|y-1|<B$ cannot contain y=0 only when $0<B<1$

Question

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

Answer 1

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 $B=1$.

Answer 2

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 $\color{blue}{0<B<1}$.