# Determine the truth value of this statement with nested quantifiers [closed]

If the domain for all variables consists of all integers.

$$\exists n \forall m(n < m^2)$$

I think the answer is false because if $m = 0$, then the statement is false, right? But the textbook gave me "true" as the answer, so I am confused...

## closed as unclear what you're asking by Chappers, Claude Leibovici, Empty, Servaes, user1551Sep 24 '15 at 10:23

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• if $m=0$ then define $n=-1$. indeed, $-1 < 0^2$ and $n < m^2$. An integer is a number without a decimal point. a "whole" number. it does not have to be positive. – Oria Gruber Sep 23 '15 at 22:36

Hint: Let $n$ be any negative integer.