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TorqueDrifter comments on Logical Pinpointing - Less Wrong
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S0 != 0
Suppose Sx != x. Then, if SSx = Sx, then Sx is the successor of both x and Sx, so x=Sx. This is false by assumption, so SSx != Sx.
Thus, by "And every property true at 0, and for which P(Sx) is true whenever P(x) is true, is true of all numbers.", for no number x is Sx=x.
Is there something wrong with this reasoning?