- #1

pissedoffdude

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## Homework Statement

If x is a real number, show that there is an integer m such that:

m≤x<m+1

Show that m is unique

## Homework Equations

Archimedean Property: The set of natural numbers has no upper bound

## The Attempt at a Solution

I'm having trouble with showing that m is unique. If x is a real number, I can find integers that are smaller and bigger than it. If m=x, then m≤x. By the Archimedean property, m+1>x and m+1>m, so m≤x<m+1