It's been years since I got my math degree, but IIRC this isn't true. At least, it's not true in enough framings that you can assert it this plainly. Infinity isn't just another number, and just because the symbols are identical in either side of the equals signs doesn't mean the entities described are.

We are talking about the floating point number format and the behavior of computer programming languages.

In “mathematics”, the meaning of the symbol ∞ depends on what number system we are talking about. In some contexts ∞ is not a “number”, but rather a shorthand for a statement about limits. In other contexts it is a number.

If you want to learn about the “affinely extended real numbers”, which is what floating point numbers more or less approximate, you can read https://en.wikipedia.org/wiki/Extended_real_number_line