- You have an assignment due today. Please hand those in.
- You also have an assignment due next Thursday -- keep an eye on the assignment page.
- Here's a little something about the logo project.
- have a little review of the procedure of "primitive counting",
- Talk about those one-to-one correspondences, and then
- find out how those Babylonians were doing math.
Notice that we write the answer starting from the 1 at the bottom (I wrap it in a triangle to distinguish it from the other remainders, which I put in boxes). So 22 is the same as 10110, obtained using "primitive counting" (aka "counting by partition").
- Use primitive counting to write 79 as a string of 1s and 0s.
- Given the string 1101001: find how we would write that number.
It's good to generalize! Explore the consequence of new ideas....
- What is "six"?
We learn something of that in From fish to infinity. But
"Six is more ethereal than six fish.... It applies to six of anything..., the ineffable thing they all have in common." So we use the counting numbers as our counting yardstick, and put them into one-to-one correspondence with a set of objects to discover its number.
- "...numbers are shortcuts for counting by ones...."
- Furthermore, "...Humphrey might realize he can keep counting forever." -- something that becomes very important whenever we have to talk about infinity.
Any two things that have the property of "six-ness" can be put into one-to-one correspondence, and that's just what Ernie did for Humphrey and his furry friend.
Did you notice Humphrey using any other cues to help him keep track of the number of fish?
Let's see if we can solve this mystery before the end of class: