This evening Katie and I were playing with functions again. We were taking turns coming up with functions and having the other person guess the rule from a few example in-out pairs. Katie was able to guess all of my functions (I didn’t have any mathematically difficult ones) and came up with a few good ones of her own. For example:
- A →Z, B→Y, C→X
- katie→eitak, zoe→eoz
- 1→10, 2→9, 3→8
For the 3rd example, when I proposed that the rule was subtracting the number from 11, Katie said that this was not correct. When I asked her what her rule was she said, “it’s the same as in the A →Z, B→Y, C→X case.”
Occasionally, Katie was coming up with not well-defined functions. For example, one time her rule was: a word goes in and a rhyming word comes out. While pointing out to her that some words have multiple rhymes, I had the thought of introducing her to not one-to-one functions and their lack of inverses. I used the example of a person being mapped to their mother; if a mother with multiple children goes in, it is unclear which child should come out. Katie’s reply: you can just have the older one come out!