Please Login to access more options.
Problem 85: (The Floor Function)
Suppose that $x$ is a real number. Use the completeness axiom to prove that there exists an integer $m$ such that $m-1\leq x<m$.
To use the completeness axiom, you'll need to create a set $S$ so that $m$ is either the infimum or supremum of the set.
The following pages link to this page.
Here are the old pages.