Given the fact that the following inequality must hold; x > y-1 For all y[tex] \in[/tex] ]0,1[ (an open interval) and given the fact that one can choose y After one chooses x, can one then state that x > 0 holds? My idea was to say that at least x >= 0 holds because: 1) Someone picks a negative x that is arbitrarily close to 0, say -0.000...001. 2) I can now choose a y from the interval ]0,1[, say 0.999999... so that y-1 > x 3) Therefore nobody can pick a negative x so that the inequality holds However, I am even more unsure about the strict inequality x > 0. It seems unlikely to me that it holds. How do you properly reason about these kind of things?