Recent content by trebolian

HallsofIvy, are you saying that the contrapositive of "for every ε > 0..." is actually "there exists an ε > 0 such that..."? I would have thought that the contrapositive should be "there exists an ε < 0 such that...", i.e switch the inequality as well as the universal/existential quantifier

Homework Statement Theorem: Let x,y,ε be ℝ. If x≤ y+ε  for every ε > 0 then x ≤ y. Write the above as a logic statement and prove it using contrapositive proof. The attempt at a solution The contrapositive statement x > y → x > y+ε is only true if ε < 0. Does a...