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## Homework Statement

Show that the function

[tex]

f(x) =\\

\begin{cases}

\frac{1}{x} &\quad 0 < x \leq 1\\

0 &\quad x = 0

\end{cases}

[/tex]

is unbounded.

## Homework Equations

If f is bounded, |f(x)| <= M for all x in f's domain.

## The Attempt at a Solution

I tried arguing by contradiction: suppose there is such an M. Then |f(x)| = f(x) <= M. But if f(x) < 1/M, f(x) > M. But I get stuck because that means

*this*particular choice of bound does not work. Instead, choose N > M. But then f(x) < 1/N makes f(x) > N. There might be a bound, and I'm having trouble proving that there is not a bound.

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