I'm working through a stats textbook and have a question of the form:

You will perform a significance test of $H_0: μ=25$ based on an SRS of $n=25$. Assume $σ=5$.

I'm stuck on the 'equals' part of $μ=25$. Given that we're working in the set of reals, isn't the probability of $μ$ equaling 25 zero? (Assume a non-textbook dataset; e.g. the odds of $μ=180$ for the height of adult humans is zero).

I think what the hypothesis is trying to say is "$μ$ is within bounds dictated by your confidence level, but mean$(μ)=25$".

The alternate hypothesis is something like $H_a: μ \neq 25$, which I know is true for any non-hypothetical dataset.

So, what does $H_0: μ=25$ actually mean?