Hello, I have decided to study analysis on my own and am starting with principles of mathematical analysis by rudin. I am having trouble understanding pg. 9 on the density of Q in R, part b. It states: If [itex]x \in R, y \in R [/itex] and [itex] x<y [/itex] the there exists a [itex] p \in Q [/itex] such that [itex]x < p < y[/itex] Proof: Since [itex] x<y[/itex], we have [itex] y-x>0[/itex] and the Archemedian Property furnishes a positive integer n such that: [itex]n(y-x)>1[/itex] Applying the AP again, to obtain positive integers m1 & m2 such that [itex]m1>nx[/itex], [itex]m2>-nx[/itex] Then: [itex]-m2<nx<m1 [/itex] Hence there is an integer m such that [itex]m-1 \le nx<m [/itex]........ Can someone explain to me the last line? Where does this less then or equal come from?