- #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