# Quantifier statement explanation

I'm having trouble understanding what the above statement means in plain English.

Does it mean: "For any Natural number there exist a number greater than it". I don't get what the right part of the implication means.

• Your interpretation is correct. What part are you struggling with? Apr 21, 2017 at 19:59
• I was confused about the $\exists y(y \epsilon \mathbb{N} \wedge x <y)$ part Apr 21, 2017 at 20:14

You are correct. Literally translated, the statement means "for all $x$ such that $x$ is a natural number, there exists a number $y$ such that $y$ is a natural number and $x$ is less than $y$".