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Old 05-20-2016, 10:05 PM
Cessh Cessh is offline
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Default 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?
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Old 05-21-2016, 01:06 AM
clarinetist clarinetist is offline
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The images of 4, 5, and 6 induced by f are undefined.
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Old 05-21-2016, 01:19 AM
Cessh Cessh is offline
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I alsoalso thought so. Does undefined means zero? Or empty?
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Old 05-21-2016, 11:04 AM
Academic Actuary Academic Actuary is offline
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If it has a different domain, then it isn't the same function.
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Old 05-21-2016, 07:37 PM
Cessh Cessh is offline
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Quote:
Originally Posted by Academic Actuary View Post
If it has a different domain, then it isn't the same function.
But isn't a function usually symbolized as a blackbox with one input and one output (like in Wikipedia), which means you can vary the input of a function but you don't actually have direct control over the output?
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; 05-21-2016 at 07:43 PM..
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Old 05-22-2016, 10:46 AM
Academic Actuary Academic Actuary is offline
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Quote:
Originally Posted by Cessh View Post
But isn't a function usually symbolized as a blackbox with one input and one output (like in Wikipedia), which means you can vary the input of a function but you don't actually have direct control over the output?
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?
Input x 7 = Output by itself is meaningless. What if your input isn't a number?
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Old 11-17-2017, 03:07 AM
Z3ta Z3ta is offline
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Quote:
Originally Posted by Cessh View Post
It doesn't change the function when I changed the domain, right?
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 isnít 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 youíre pointing out that they are all restrictions of a single familiar function.
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