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#1 2007-10-30 08:38:47
- xXxEmZyxXx
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- Registered: 2007-10-15
- Posts: 12
surjective function
let A B be sets
f:A->B
suppose there is a function h:B->A with the property that f(h(b)=b for all bEB
show that f has to be surjective
please help will be much appreciated!!!
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#2 2007-10-30 09:03:15
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: surjective function
For all b ∈ B, c = h(b) ∈ A and f(c) = b. That is all. QED
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#3 2007-10-30 10:17:37
- MathsIsFun
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- Registered: 2005-01-21
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Re: surjective function
Also see: Injective, Surjective and Bijective
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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