Need help with a proof guys:

Prove that { $${ x \in \mathbb{R} : x^{2} \le x} $$ } = [0,1].

Its the beginning of the course, so I assume this should be relatively straightforward. Would it be better to approach this using just properties of the ordered field? Proof by contradiction or proof by induction? Any tips on getting started would be appreciated!

Question

Need help with a proof guys:

Prove that { $${ x \in \mathbb{R} : x^{2} \le x}  $$ } = [0,1].

Its the beginning of the course, so I assume this should be relatively straightforward. Would it be better to approach this using just properties of the ordered field? Proof by contradiction or proof by induction? Any tips on getting started would be appreciated!

anonymous · Answer

r u studying abstract algebra too?????

anonymous · Answer

This is for Introduction to Real Analysis.