How to prove that for all $x$ there exists some $y$ where $ (x^2 + y^2 \geq 0)$?

Question

How can I prove that $\forall \,\,x\,\,\exists y\,\,,(x^2 + y^2 \geq 0)$?

Answer 1

In fact, if $x \in \Bbb R$, for any $y \in \Bbb R$, especially let $y=0$, it always hods.

Answer 2

Easy solutions:

• $y=0$

• $y=1$

• $y=x$

The second one gives you $x^2+y^2>0$.