A map is a way of associating unique objects to every element in a given set. A map from to is a function such that for every , there is a unique object . The terms function and mapping are synonymous for map.
The notation specifies the domain and codomain . The barred arrow , called the maps-to arrow, instead specifies the value assigned to an element, as in for (Lang 2002, p. ix).
More things to try:
Weisstein, Eric W. "Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Map.html
from 
to 
is a function 
such that for every 
,
there is a unique object 
.
The terms function and mapping are synonymous for map.
specifies the domain 
and codomain 
. The barred arrow 
,
called the maps-to arrow, instead specifies the value
assigned to an element, as in 
for 
(Lang 2002, p. ix).
