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 = b1. 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

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