Thread: Real analysis proof

let 0<x show that there is a unique m in N such that m-1 < or = x < m.
the book says to consider n in N : x < n and that N is well ordered

Originally Posted by mtlchris

let 0<x show that there is a unique m in N such that m-1 < or = x < m.
the book says to consider n in N : x < n and that N is well ordered

For , consider the set . By the well ordering principle, this set has a unique smallest element. Call this element .

because . because if it isn't, then , contradicting the fact that .