Precise statement of the intermediate value theorem

[Imum Coeli]

Hi I was just wondering if this makes sense?

If \(\displaystyle f:[a,b] \mapsto \mathbb{R} \) is continuous, then \(\displaystyle \forall \; y_0 \in f([a,b]) \; \exists \; x_0 \in [a,b] : f(x_0)=y_0 \)

mainly this part
"\(\displaystyle \forall \; y_0 \in f([a,b])\)"

Thanks.

 

[mattosd1]

yes