---
tag: 0KT8TGXD8K
kind: concept
name: Equivalence relation induced by a function
aliases: [kernel-of-a-function, equivalence-kernel]
msc: ["03E20"]
sources:
  - url: https://en.wikipedia.org/wiki/Kernel_(set_theory)
    locator: lead section
same_as:
  wikidata: Q687704
  wikipedia: Kernel (set theory)
---

## Summary

Each function induces an equivalence relation on its domain: two elements are equivalent when the function has the same value at both.