Note that software isn't mathematics - it's language (as in English)....

Nope.

The language in question is mathematics, not "as in English".

It is exact. An expression in mathematics isn't variable. It always has the same exact meaning.

English evolves over time. The definitions of the language drift as usage changes. You can't easily read Old English - it is nearly senseless from the point of view of modern English - yet is is still "English".

Doesn't happen with Mathematics. If you change the definitions, the program doesn't work.

This is sort of what happens if you take a program from one platform to another without re-translating into the target platform. You are changing the definitions going from an Intel structure to an ARM. You must first translate the program into the language of the target.

The two languages are mathematically equivalent - which is why you get the same results (within the limits of the target). Yes, floating point answers may not be quite the same - but that is because the target language is slightly different. The abstract mathematics is identical, even if the IMPLEMENTATION of the mathematical machine is slightly off. That is the difference between the hardware reality and the abstract math.

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