Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.


share|cite|improve this question
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
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. $1 + 1 = 2 \cdot 1$).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.