Indicator function
Date: 2025-11-30
Let function f: {a,b,c,d} → {0,1} such that it maps:
a → 1
b → 0
c → 0
d → 1
f is a 2-valued function (outputs 2 values). Such a function is called a condition, and for one of the two values, the condition is considered satisfied.
Usually, when using "1" and "0" designations, "1" is considered to indicate that the condition is satisfied.
The notation {variable | condition or list of satisfied conditions} defines a set through a list of conditions.
Let's define a new set using f:
{x | f x} which is equivalent to the set {a,d} because f is satisfied for a and d, that is, when evaluating f a and f d we get 1.
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