Definition: Indicator (Characteristic) Function, Carrier

Let $S$ be a set. An indicator function (or characteristic function) $\chi$ on $S$ is a function $\chi:S\to\{0,1\},$ i.e. a function mapping each element of $S$ to exactly one of the two values $1$ or $0.$

For a given characteristic function $\chi$, the fiber of $1$ under $\chi$ is called its carrier.

Notes

Example

The carrier of the set of integers in the set of real numbers:

def carrier(N): if N==floor(N): return 1 else: return 0 points= [(i, carrier(i)) for i in range(-5,10)] list_plot(points)

Explanations: 1 2
Proofs: 3 4
Propositions: 5


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References

Bibliography

  1. Flachsmeyer, Jürgen: "Kombinatorik", VEB Deutscher Verlag der Wissenschaften, 1972, 3rd Edition