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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:
( OMEGA v)µ'x= OMEGA v×µ'x Def.
 OMEGA 2×2'x = ( OMEGA 2)2'x = ( OMEGA 2)1+1'x =  OMEGA 2' OMEGA 2'x =  OMEGA 1+1' OMEGA 1+1'x
= ( OMEGA ' OMEGA )'( OMEGA ' OMEGA )'x =  OMEGA ' OMEGA ' OMEGA ' OMEGA 'x =  OMEGA 1+1+1+1'x =  OMEGA 4'x.


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