Write using quantifier notation.

Question

"There is one and only one real solution to the equation x^3 + x + 1 = 0"

Could someone please explain to me how to write this using quantifier notation?

Answer 1

$\exists !x \in \mathbb {R} (x^3+x+1=0)$

In MathJax/TeX, "\exists !x \in \mathbb {R} (x^3+x+1=0)"

Answer 2

This one might serve the purpose.

Answer 3

If you can't use the $\exists !$, use:

$$\exists x \in \mathbb {R} \ \exists y \in \mathbb {R}(y^3+y+1=0 \leftrightarrow y = x)$$