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>I'm keen on a distinction between numbers and forumals.

What’s the operational advantage of this approach? I feel like it would wreck havoc with fundamental tools like mathematical induction..

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The difference between f(x)=...=0 and x=2, e.g. is quite huge for a lot of college students. The distinction between constants, operators and formulas is quite explicit in algebra. It seems to be a natural distinction to make. One advantage, I guess, is that a formula can be wrong, but a number can't, which is why proof by induction works at all.

How would a proof by induction work with only two natural numbers?

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