Definition
For the formal definition, let X and Y be sets and let f be a function from X to Y. Elements x1 and x2 of X are equivalent if f(x1) and f(x2) are equal, i.e. are the same element of Y. The kernel of f is the equivalence relation thus defined.
The kernel, in the equivalence-relation sense, may be denoted "=f" (or a variation) and may be defined symbolically as
Read more about this topic: Kernel (set Theory)
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