Ah, so I think @Elzear_Young you are arguing that the normal distribution is a probability density function, so without talking about a region of x, we can’t sum over it to get a probability mass.
We actually had that discussion before, and I would highly suggest you to perhaps go through that again or just read my conclusion. This link will bring you to my conclusion of the discussion but please start from the first post of the thread if you prefer to. It would take some time to read the whole thread but it would worth it if we had covered all your concerns.
Cheers,
Raymond