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Let P(x) be the statement "x + 1 = 2x" domain is all integers, what is the truth value?

$\exists x P(x) (E should be backwords...)

I know how to do P(0). But how exactly do I do this one? I wouldn't just want a True or False. Please explain how I can figure this out, and how I should read it.

Thanks!

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If you mean $\exists$, it is read "there exists," so that $\exists x$ would read "There exists an $x$ so that $P(x)$." –  Clayton Jan 24 '13 at 3:35
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1 Answer

up vote 2 down vote accepted

$P(x)$ is not a statement. It is a predicate, meaning its truth value depends on $x$. You cannot assign a truth value to a predicate without specifying the input.

$\exists x P(x)$ is a statement. It means "There is at least one particular $x$ such that $P(x)$ is true." This is a true statement, since $P(1)$ is true (i.e. $1 + 1 = 2 \cdot 1$).

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