Would i be ok to use base step as n = 1 for a function A -> B for one in A
A (x) mapping to B (a1,a2,a3.... am)
No of functions possible for n-1 is m^n
I dont know how to go on with the induction step any ideas?
Would i be ok to use base step as n = 1 for a function A -> B for one in A
A (x) mapping to B (a1,a2,a3.... am)
No of functions possible for n-1 is m^n
I dont know how to go on with the induction step any ideas?
Suppose . A single map from is a map from a set with n-1 elements to a set with m elements. By the induction hypothesis, there are possible functions that map to . For any of those maps, we need to choose what maps to in order to extend the function to a function from . We have elements of B to choose from, completely independent from the choices for the mappings of . Thus, for each such map, we have different functions that extend the map to a map to all of . Then, there are total functions from .