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Topology and functions

Topology
Sets and Functions (XXXIII)
Functions

Two mappings f : X --> [Y and g : X --> Y are said to be equal ( and we write this f = g )
if f(x) = g(x) for every x in X. Let f, g and h be any three mappings of a non-empty set X
into itself, and show that multiplication of mappings is associative in the sense that
f(gh) = (fg)h.

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This solution is comprised of a detailed explanation that multiplication of mappings is associative in the sense that f(gh) = (fg)h.
It contains step-by-step explanation of the following problem:

Two mappings f : X --> Y and g : X --> Y are said to be equal ( and we write this f = g )
if f(x) = g(x) for every x in X. Let f, g and h be any three mappings of a non-empty set X
into itself, and show that multiplication of mappings is associative in the sense that
f(gh) = (fg)h.

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