It’s true cheating, but if you assume the Peano axioms, you can write any integer with one zero without having to resort to complex functions such as √. For example (if I didn’t miscount the S-es or parentheses),

  S(S(S(S(S(S(S(0)))))))) = 7

▲ rav 16 hours ago | parent [-]

You don't even need zero in that case, you can use the fact that 2 - 2 = 0 to use the four 2s:

  S(S(S(S(S(S(S(2+2-2+2)))))))) = 7

...which is essentially the same as Dirac's general solution (which also derives a "successor operator" akin to S that doesn't spend any numeric literals).

EDIT: I realize that this was already posted in a comment by shoo several hours ago.

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vessenes 16 hours ago | parent [-]

You’ve got S(4) in the center there

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jasomill 12 hours ago | parent | next [-]

From the text, the inner term was clearly intended to be "2-2+2-2".

	▲	vessenes 4 hours ago \| parent [-]
		I agree!

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16 hours ago | parent | prev [-]

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