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## Homework Statement

Let a,b be any real number. Show that if a-e < b for any e > 0, then a <= b.

## Homework Equations

## The Attempt at a Solution

I tried a proof by contradiction, that if a>b then we violate some assumption.

Here it goes:

Suppose not.

Then a > b.

a- e > b - e

Since we assume a-e < b, thus b > b-e. But well...this seems right. Where did I go wrong?