Convention on infinity comparision

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What's the difference between $-\infty \leq a \leq \infty$ and $-\infty < a < \infty$ conceptually or otherwise.

It doesn't really affect the solution to the solution of this problem I'm working out( I hope) but the solution states $\leq$ and I have $<$ . So I would appreciate an explanation on how are they different.

Thanks and regards.