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#1




Function definition in set theory.
This is a tricky question
Let's define a function F as f:A>B where domain A is the set {1, 2, 3} and codomain B is the set {7, 8, 9}. So that f(1)=7, f(2)=8, f(3)=9 Now let us take the same function f and give it a domain {1, 2, 3, 4, 5, 6}. What would the output (image) of this function be? 
#2




The images of 4, 5, and 6 induced by f are undefined.
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#4




If it has a different domain, then it isn't the same function.

#5




Quote:
and btw how do you know it's not the same function? It could be the same function. For example if I say the first domain was for positive integer numbers and in the second domain it was for negative integer numbers. And the function is still let's say x multiplied by 7. It doesn't change the function when I changed the domain, right? Last edited by Cessh; 05212016 at 07:43 PM.. 
#6




Quote:

#7




Yes it does. A function is defined by its domain, codomain and the assignment of each element of the domain to an element of the codomain. Change any of those three things and it is a different function (that includes just throwing in another element of the codomain that isn’t mapped to).
What you are describing could be thought of as restricting the function to subsets of the domain. You are still defining different functions even though you’re pointing out that they are all restrictions of a single familiar function. 
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