Prove both by method of contrapositive.
1. If a ≤ b + ε, where ε > 0, then b > a.
2. If 0 ≤ a - b < ε, where ε > 0, then a = b.
I'll start with problem 1.:
p: If a ≤ b + ε, where ε > 0
q: b > a
neg q: b < a
neg p: for some ε' > 0 1/2(a - b), a > b + ε'
define ε' = 1/2(a - b)
I...