I disagree with the author. He confuses Math with Computer Science. In Math, a x b and b x a are both equal and equivalent. The division example with switching places is ridiculous. Learning from mistakes is part of the process. Even kids who suck at Math won't switch places when dividing or subtracting!
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In math, a x b and b x a are equivalent only when dealing with commutative (a.k.a. Abelian) operations. If a and b are matricies then the above does not hold. Consider:
a = [1, 2]
b = [ 3 ]
[ 4 ]Again, Computer Science! There's no such thing as "dynamic type variables" in Math!