Homework Statement
S≡{x|x∈ℝ,x≥0,x2 < c} Prove Sup S = c
Homework EquationsThe Attempt at a Solution
Since x in the set real numbers, there are two cases for x: x < 1 or 0 <= x <=1
if 0 <= x <=1, then x < c + 1 since c is positive.
if x < 1, then x^2 < c < x*c + x = x(c+1)
thus x < c+1, by the...