1. The problem statement, all variables and given/known data Suppose that , for any $$ \epsilon > 0, a < b + \epsilon $$ . Then $$ a\le b $$ 3. The attempt at a solution I have the proof, its not a question that was assigned to me, it was an example used. According to the proof i can choose ANY epsilon greater than 0, so lets choose 10. then 2 < 1 + 10 = 11. Right? Then $$ 2 \le 1 $$ . NOT right. it's late here in the UK, is it me?