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For questions about the teaching of the function concept, function properties, and various types of functions.

2 votes

Should we teach functions as sets of ordered pairs?

Here is a comment from a colleague: defining functions as sets of ordered pairs may not be so important on its own, but it's a convenient way to learn that functions are a special kind of binary relation …
Mike Shulman's user avatar
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20 votes

Should we teach functions as sets of ordered pairs?

Moreover, I feel it's almost totally unnecessary because in practice in mathematics we do always treat functions as rules. … Similarly for (2), the criterion for equality of functions could be presented as parallel to, rather than derived from, the criterion for equality of sets. …
Mike Shulman's user avatar
  • 6,680
28 votes
12 answers
3k views

Should we teach functions as sets of ordered pairs?

exposure to functions has usually been limited to the partial $\mathbb{R}\to \mathbb{R}$ variety). … The question is, how do you "define" functions? …
Mike Shulman's user avatar
  • 6,680