Ranges and Codomains

The domain of a function can be seen as the first coordinate of an ordered pair, and the range cam be seen as the second coordinate. Thus for the ordered pair (3,5) 3 is the domain, and 5 is the domain. Every function can only have one domain and one range. Even though functions can have many many ordered pairs.

There can be, however, many co domains, as long as the function is a subset of the codomain. Consider the example:

A = {4,5,6}

B = {2,5,7}

Then the following two sets are functions of A and B with different codomains.

f1={(4,2),(5,5),(6,7)}

f2={(4,5),(5,7),(6,5)}

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