Help please.

ancientspace

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Sep 24, 2014
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I am not 100% sure this is the right forum but I will ask here .
Cardinality of A=m
Cardinality of B=n, how do I show that the number of functions that can form is n^m?
Btw,this was a definition our teacher gave us at Bijectivity.
Sorry for my bad english,I am not a native english speaker :rolleyes:

I need to know why that is equal to |n|^|m| distinct functions
 
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Let A={a1, a2, a3} and B=(b1, b2, b3, b4). Now a function from A to B is a mapping of an element in A to a unique element in B. However, the element in B may be chosen many times. So

a1 can map to either b1, b2, b3, or b4
a2 can map to either b1, b2, b3, or b4
a3 can map to either b1, b2, b3, or b4

How many is this? What is the cardinality of A? What is the cardinality of B? Can you generalize how you would compute the possible number of functions mapping A, with cardinality m, to B, with cardinality n?

BTW: not all of those mappings are bijective

Edit: Although correct, you do not have to use the magnitude of m raised to magnitude of n, |n||m| since the cardinality of a set is a member of the set of non-negative integers. Also corrected typo
 
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