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Imagine, for instance, we have a set that has all of the possible domains and ranges of every possible combination of inputs of a function.

Here's an example:

The equation for Polytropes in astrophysics:

Polytrope Equation

Here's the, what I like to call, the animated "Graph space", or set of the domains and ranges:

Polytrope “Graph Space”

What is the name of the data described by this animation?

Asaf Karagila
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Armend Veseli
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    Not everything has a name – Mariano Suárez-Álvarez Dec 02 '22 at 18:11
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    Given some function $f: A \to B$, the graph $G$ of $f$ is $G = {(x,y) : x \in A, y = f(x)}$. You are asking for "the set of all possible domains and ranges of every possible comination of inputs of a function," which is not entirely clear. I suspect you are asking for the powerset of $G$? – RyRy the Fly Guy Dec 02 '22 at 18:11
  • @RyRytheFlyGuy I believe this is correct, as far as my knowledge of this topic goes. – Armend Veseli Dec 02 '22 at 18:18
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    The animation you linked would probably best be described as a "parameterized function", but that's not at all what you've asked for in your first paragraph. – JonathanZ Dec 02 '22 at 18:24

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Given some function $f:A \to B$, the graph $G$ of $f$ is $G=\{(x,y):x\in A,y=f(x)\}$. I suspect you are asking for the powerset of $G$. This would be the set of all possible subsets of $G$. You could think of it as the set of all possible subsets of inputs into $f$ such that each input $x$ is accompanied by its corresponding output $f(x)$.

RyRy the Fly Guy
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  • So it is also a parameterized function encompassing all variables? – Armend Veseli Dec 02 '22 at 18:33
  • I would not equate a powerset with a function. you seem to be asking two separate questions in the title of the post and within the post itself. Are you trying to figure out what to call the animation? – RyRy the Fly Guy Dec 02 '22 at 18:41
  • No, I am trying to find a name for all of the domains and ranges with every possible value for every possible variable of a function. – Armend Veseli Dec 02 '22 at 20:48