We have a multiply that works everywhere with the same efficiency, as long as we use irrational fractions. But we invented multiply to make groups of finite things, that is its purpose. Eventually, the density of finite things and the density of groups clash, that is all.
It appears in physics because we map observations to sets of finite things. It just so happens the vacuum is finite in density, and it uses the speed of light to multiply. So when physics is accurate, then physics had 'powered up' their integers to match the vacuum integers.
We could write the
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