- #1

k3k3

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## Homework Statement

Let f be the function defined f(x)=1/x. Prove that f is not bounded on (0,1)

## Homework Equations

## The Attempt at a Solution

I think I should prove by contradiction.

Assume f is bounded on (0,1).

Since f is bounded, there exists a real number M such that |f(x)| ≤ M for all x in (0,1)

f(x) will never be negative since it is on the interval (0,1), hence |f(x)| = f(x)

This is where I begin to get unclear on where to go next. I want to show that M+1 ≤ M

Is it correct to use 1/(M+1) and plug it into f(x)?