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Undid revision 1231433054 by 50.220.179.25 (talk) NOTAFORUM gibberish inserted into almost 20-year-old thread |
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: You're reading too much into the definition. g(f(x))=x only says that g is a ''left inverse'' of f (not a total inverse since f may not be 1-to-1). That is, given y it returns some value z such that y=f(z). If f maps two values to y, g should return one of these two values, but we don't care which. In your example, the identity function g(x)=x is a left inverse of f(x)=x%5 [[User:Blokhead|Blokhead]] 13:50, 12 June 2006 (UTC)
: Bah, I should check the definitions before I post... anyway, the idea is the same, but notice how f^{-1}(f(x)) is used as a ''set of values'' in the definitions, not a single-valued thing. f^{-1}(y) is the set of all x's that f maps to y. Again, the algorithm could return any one of these, we don't care which. Forget what I said about left inverses.. [[User:Blokhead|Blokhead]] 13:54, 12 June 2006 (UTC)
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