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6.24

The method by which mathematics arrives at its equations is the method of substitution.

For equations express the substitutability of two expressions, and we proceed from a number of equations to new equations, replacing expressions by others in accordance with the equations.

6.241

Thus the proof of the proposition 2×2=4 runs:
(^v)^µ'x=^v×µ'x Def.
^2×2'x = (²)²'x = (²)¹⁺¹'x = ²'²'x = ¹⁺¹'¹⁺¹'x
= (')'(')'x = ''''x = ^1+1+1+1'x = ⁴'x.