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Combinatorial Theory (f*h=g*h) g=f? 
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#1
Oct1211, 08:32 PM

P: 24

1. The problem statement, all variables and given/known data
If f :X > X and g:X > X are functions, and h:X > X is a onetoone function such that f * h = g * h need it be the case that f = g? Prove it or give a counterexample. What if, in addition, X is finite? 3. The attempt at a solution I know that f does not equal g for an infinite set but is for a finite set. I know to prove that it isn't when it is infinite set it is the difference between the onto function. I am not sure how to relate that to the problem and build a proof out of it. Thanks! 


#2
Oct1211, 08:55 PM

P: 7

Yes, g must equal f in your example, i do not have time to answer your question fully, but I would first say you have not correctly defined a onetoone function appropriately. Look into defining similarity of classes of a one to one relation.



#3
Oct1211, 09:29 PM

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#4
Oct1211, 11:29 PM

P: 24

Combinatorial Theory (f*h=g*h) g=f?
I am not sure where to go from here. I understand all the basics of onto and one to one functions but am struggling to apply them here.
What I have: X is an infinite set, h is a one to one function, but not an onto function. Thus when using the function h, the two infinite X sets do not have matching ranges. Thus, there could be two different h values and so f does not have to equal g for infinite sets. When X is a finite set, and h is one to one, then it has to be onto, thus stating that through the function h, the number is equal to it's output and thus h=h and so f has to equal g. Is that right? I feel like I am missing something. Thanks again for all your help! 


#5
Oct1311, 09:48 AM

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