∀x (x > 0 → ∃y ((√x)/y = 3))
I've learned about different types of proofs, and I'm thinking here that I would first negate the statement to then prove the negation. Would the negation be: ∃x(x ≯ 0 → ∀y((√x)/y ≠ 3)) ?
If it's as easy as finding a number for x in which the statement is false, I could say:
let x = 25
(√25)/y = 5/y ≠ 3
Is this sufficient proof?
In either case, how would the proof be different with integers than with real numbers? Thanks ahead.