Proving that 1=2, is Oracle Wrong to Short-Circuit an Execution Plan?

December 25, 2009

Earlier this month I wrote a blog article that showed how Oracle behaves when the WHERE clause includes the predicate 1=2.  But is the shortcut implemented by Oracle wrong?  Will 1=2 never happen?

I attended a college course that covered just mathematical proofs (the name of the class escapes me at the moment – Discrete Mathematics?).  The mathematics professor for that course proved that 1=2.  That proof follows (I attempted to align the equal sign to make the proof easier to read):

Assumption: Let a = b
1.  a^2               = a^2
2.  a^2               = b^2
3.  a^2               = b * b
4.  a^2               = a * b
5.  a^2 - b^2         = a * b - b^2
6.  (a + b) * (a - b) = b * (a - b)
7.  a + b             = b
8.  b + b             = b
9.  2b                = b
10. 2 = 1

 

Mathematical Explanation of the Above Steps:
1.  Truth Statement
2.  Substitution
3.  Factor
4.  Substitution
5.  Subtract b^2 from Both Sides of the Equation
6.  Factor
7.  Divide Both Sides of the Equation by (a - b)
8.  Substitution
9.  Simplification
10. Divide Both Sides of the Equation by b

I think that there is a lesson in the above that may be applied to the understanding of Oracle databases.  Let me ponder the lesson while you review the Faulty Quotes series of blog articles.

A couple references for mathematical proofs follow – how might the techniques of mathematical proofs be applied to understanding the logic built into Oracle Database?http://www.eiu.edu/~mathcs/mat2345/index/Webview/Slides/handout-Week02-2×3.pdf
http://www.math.harvard.edu/archive/23b_spring_05/proofs.pdf
http://en.wikibooks.org/wiki/Category:Mathematical_Proof
http://wapedia.mobi/en/Inductive_proof