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A comment on Nix the Tricks: Math tricks defeat understanding. Parent comment

Re:Nix the Tricks: Math tricks defeat understanding by robryk on Sunday September 27, 2015 @10:29AM (#10286604)
As long as your steps are implications in the reverse direction (from the later to the earlier statement) this is perfectly correct. In most cases I've seen people do that the transformations are actually equivalences, which muddies the waters somewhat.

What is a problem is when people do use reverse-implications that are not equivalences, arrive at something false, and claim that the original equation is false.

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Re:Nix the Tricks: Math tricks defeat understanding by a-nikolaev on Sunday September 27, 2015 @01:09PM (#10287151)
Yes, I know ) But then this whole derivation now lives in a "special world", where you cannot do all math, but only certain subset.

Your example is cool. I have not seen many exmaples of such logic, but people probably do it too.. )

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Re:Nix the Tricks: Math tricks defeat understanding by robryk on Sunday September 27, 2015 @02:53PM (#10287485)
The most common example of such logic is multiplying by maybe-zero (transforming a=b into ac=bc) and factoring out a possibly-zero factor (transforming ac!=bc into a!=b).
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