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Originally Posted by glatt
since a=b, then (a-b) = (a-a) = 0
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It is called the trivial solution.
a * c = b * c
has a unique solution (for real numbers) EXCEPT when c = 0. We tend to forget the other part of that algebraic relationship: that c cannot equal 0. Once c becomes zero, then any number can equal any other.
Naive will then proclaim that math can be manipulated - another interpretation of "lie, damn lies, and statistics". Instead, by providing only a half fact (by forgetting the part where c cannot equal zero), then a mistake occurs.
c=0 is called the trivial solution; an overlooked mathematical error that glatt has successfully identifed.