What is the generic term for domain & range?

In summary, the domain in mathematics refers to the set of all possible input values for a function or equation, while the range refers to the set of all possible output values. These terms can be encompassed by the generic term "input-output set" or "input-output values". It is possible for the domain and range to be the same for a function, particularly in the case of a one-to-one mapping. The domain and range are closely related in a function, as the domain determines the possible input values which in turn affect the range, or possible output values.
  • #1
swampwiz
571
83
As I understand it, there are the terms:

domain - variables that are input to a function

range - the variable that is output to a function

This works well in a canonical single equation system like z = f( x , y ), but breaks down in an implicit function or set of equations. I was wondering what the proper term is for all the variables that exist in any system of equations - whether they happen to be input or output for any particular equation.
 
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  • #2
Locus if we a talking about geometry. Otherwise "solution set" or something similar.
 

FAQ: What is the generic term for domain & range?

What is the definition of "domain" in mathematics?

In mathematics, the domain refers to the set of all possible input values for a function or equation.

What does "range" mean in mathematical terms?

In mathematics, the range is the set of all possible output values for a function or equation.

Is there a generic term that encompasses both domain and range?

Yes, the generic term for both domain and range is "input-output set" or "input-output values".

Can the domain and range be the same for a function?

Yes, in some cases, the domain and range can be the same for a function. This typically occurs when the function is a one-to-one mapping.

How do the domain and range relate to each other in a function?

The domain and range are closely related in a function, as the domain determines the possible input values which in turn affect the range, or possible output values.

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