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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.

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

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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 $y$".

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