Monday, January 24, 2011

A Simple Example of Referential Opacity

It results from correctly applying the product rule: 

Proposition: 6 = 5.
Proof.  

[1] 5 = 2+3
[2] 6 = 2x3
[3] 3 = 2+1
[4] 6 = 2x2+1 (by substitution, result of [3] for part of [2])
[5] 2x2+1 = 4+1 = 5
∴ 6 = 5 QED