Two mathematicians Fred and Fran were having a baby girl, their first child! They sought the perfect name, a name that would simultaneously reflect togetherness, relationships, and individuality in their burgeoning family. Day and night they debated, rejecting name after name. Finally, they had it! The perfect name!

They named her Erin.

Why?

[Yootleoffer: 1 Yootle for first correct response.]

• 2008/06/18 Addendum: Fred and Fran both study set theory.
• 2008/07/27 Addendum: It turns out I didn’t need the 6/18 hint-addendum: commenters had already chimed in with correct answers but, due to a combination of mechanical and pilot error, I didn’t realize it.

  So, … drum roll please…
  the winner is… John! His is the first correct response. Commenter d is also correct with a more succinct and mathematical explanation. Dennis is close but not quite complete. So I’ll award John 2 yootles, d 1 yootle, and Dennis 1/2 yootle. John and d please let me know your contact info to claim your bounty.

  Dennis asks what a yootle is worth. A yootle is a quantified “thanks, I owe you one”. So it’s worth a return favor from me, someone who trusts me, someone who trust someone who trust me, etc.

  Bonus challenge: come up with a family of four with the same property and reasonable names (necessarily of eight letters each).

• 2008/08/13 Addendum: The bonus round winner is… aj! He hacked up a script and discovered one of apparently many possible “perfectly” named families of four. Details are in the comments of this post. Thanks aj!