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Homework Statement
Prove the following propositions:
1) ∀x ∈ (0, 1), ∃y ∈ (0, 1), x < y
and
2) ∀x, y ∈ R, if x < y, then ∀b ∈ (0, ∞), ∃a ∈ (0, ∞),
x + ab < y.
Can anyone help me out with either one?
I have a few others that I can get but I can't get these two. Mainly because these don't have a specific method to use so I don't know which to use. Where as previously the ones said prove by contradiction etc.
Methods that can be used:
Direct Proof
Contraposition
Contradiction
Homework Equations
1) ∀x ∈ (0, 1), ∃y ∈ (0, 1), x < y
and
2) ∀x, y ∈ R, if x < y, then ∀b ∈ (0, ∞), ∃a ∈ (0, ∞),
x + ab < y.
The Attempt at a Solution
How would I know with method to use for these?