0

This is a really quick doubt, i'm just curious about how it will be. Imagine an equation like $\cos(x)=\sqrt{-1}$, it obviously doesn't have solutions over the reals, how do I express it symbollically? (e.g using mathematical language, as $\exists$ or $\not\exists$, etc.) I've thought of something like $\not\exists x\in\mathbb{R}:\cos(x)=\sqrt{-1}$?

Xetrez
  • 358
  • 2
    ${x\in\Bbb R~:~\cos(x)=\sqrt{-1}}=\emptyset$ is another option. That is to say, the set of solutions to the equation is empty. – JMoravitz Dec 02 '20 at 15:25
  • oh thanks! my attempt was correct too? – Xetrez Dec 02 '20 at 15:25
  • 2
    Yes, what you wrote was correct, but I think writing it in words is best. – saulspatz Dec 02 '20 at 15:47
  • i want to learn more about mathematical language and stuff like this, does this topic have a name to investigate on it more? – Xetrez Dec 02 '20 at 15:59
  • 1
    First-order logic, or predicate logic. Also, I think the best notation here will be $\forall x \in \mathbb R: \cos(x) \neq \sqrt{-1}$ (although it's closer to "no real is a solution" than to "there are no real solutions"). – mihaild Dec 02 '20 at 17:24

0 Answers0