Juan C.

asked • 29d

Express statement in using quantifiers

I can see that it is straight forward when we have an statement like: "For all x, there exists a y, such that f(x,y) = 0", which I can re-write as: "∀ x ∃ y f(x,y) = 0". But, for example, when I have a statement like:

(1) "If x, y ∈ A, then x > y implies f(x) > f(y)"

(2) "Given a > 0, there exists N ∈ N such that for all x ∈ A, n ∈ N implies | fn(x) - f0(x)| < a."

How do I handle these type of cases?


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