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Monday, November 9, 2009

Remembering Function Definitions

OK I know this is both paternalistic and heterocentric. However, if you need a good way to demonstrate Function, 1:1, and Onto, "A School Dance" gets the job done.

I give them a sheet with these slides and ask them to conjecture about the definitions.


  1. I'm more worried about students making inappropriate comments about "onto".

  2. Hi Kate,

    Does the first slide actually count as a function? I'm worried about the little blue stick figure in the top left corner -- he doesn't get assigned to anybody. Does that mean he's not in the "School Dance" domain?

  3. @Regular it depends who you ask. Computer science people don't require a relation to cover every element of the domain to be a function, and they speak of "partial" and "total" functions.

  4. Yep. Lonely dude is a problem. I suck.

    Here is what my dark overlords in Albany say:

    function : A rule that assigns to each number x in the function's domain a unique number f(x).

  5. but dammit a function is a set of ordered pairs.

    and if numbers had anything to do with it
    the the kids at the dance don't qualify.

    unapolgetic made a related point in my blog

    computerheads are of course wrong.
    all functions are total functions.
    i'm just a bigot that way.

  6. anyhow your overlords are on shaky ground
    philosophically because of the recursive nature
    of their definition. to know what a function is,
    one evidently has to know what "the function" is.
    gnu's not unix! turtles all the way down! repent!

  7. They're the mayor of shaky philosophical ground.


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