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)
Famous quotes containing the word definition:
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
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—Elaine Heffner (20th century)