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We can write a function $f:X\times Y\to Z$ as $\tilde f:X\to (Y\to Z)$. This is called “currying”.

We can also write an element of a power set $Y\in \mathcal P(X)$ as $Y:X\to \{0,1\}$. It’s somewhat similar to currying.

Is there a term for representing the element of a power set as a function like this? A verb, like “currrying”?

user56834
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    There is no special name for this and I don't see the connection with currying (a name that is rarely used in mathematics). – Najib Idrissi Feb 10 '19 at 11:30
  • Actually, the name currying would be used for subsets of $X\times Y$, since they can be written as $X\times Y \to {0,1}$, currying exhibits the mas, e.g. $X\to {0,1}^Y$ – Maxime Ramzi Feb 10 '19 at 11:39
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    The function in question is usually called the "characteristic function" or "indicator function" of the set. – Carl Mummert Feb 19 '19 at 02:13

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