Is $∃!x(x^2 = 1)$ true?

Question

for a question that I have it is asking for the truth value of $∃!x(x^2 = 1)$ my instincts tell me no because there are 2 values that make it true. Am I right?

It depends upon your universe. If you are dealing with integers then you are correct. If you are dealing with natural numbers then we can no longer consider negative values. — John Douma, Aug 11 '21 at 21:38

score 5 · Answer 1 · answered Aug 11 '21 at 21:38

5

It depends on $x$. If $x > 0$, or $x < 0$ then it's true. But if $x$ is any real number or complex number, then it's false since there are $2$ answers: $x = \pm 1$. And let's say if $x < -3$, then there is no solution.

answered Aug 11 '21 at 21:38

Wang YeFei

6,390

Also, if $x>1003$, then there exists no solution. – Antonio Aug 11 '21 at 21:46
It's an XOR situation – egglog Aug 11 '21 at 21:48

Is $∃!x(x^2 = 1)$ true?

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