Does the interval $[-c,\infty)$, with $c>0$, contain $-\infty$?

Question

I think my question boils down to some kind of definition, which I am not aware of.

Does the interval $[-c,\infty)$, with $c>0$, contain $-\infty$?

On the one hand, $c\to +\infty$ is possible; but, on the other hand, I fixed $c$ as $c$.

Thank you in advance.

Answer 1

The definition you're missing is that of a 'real number'. Infinity is not a real number, but merely an expression to denote that a sequence does not converge.

If you let $c$ go to infinity, you eventually include any of the numbers not in your original interval, so the resulting interval will contain all the (existing) real numbers, but not the (non-existent) "number" $-\infty$.

Answer 2

Assuming your interval is in the real numbers, "infinity" is not contained in any interval. Intervals on the real line consist of elements which are real numbers. $\infty$ is not a real number.