Intro Question: We've all seen the mailboxes here at Bennington. From my estimation, there's about 800 of them. Imagine they are all in a line, from #1 to #800.
To start term, they are all empty.
The first student who gets to Bennington sees a stack of papers and says "If a box is empty, I'm going to put a piece of paper in it. If it has something in it, I'm going to remove it.
The second student comes along and says: "I see the first person's rule. But I'm only going to do it every other box." So (2, 4, 6, 8, 10 ...)
The third student says: "Same rules, but every third box." So (3, 6, 9, 12 ...)
All 800 people on campus do this.
1. After the 800th person, which boxes have paper in them?
2. BONUS: Which box was used (either putting a paper in or taking a paper out) the most? <-- I don't know the answer to this one yet.
From there:
Types of numbers.
natural/counting -- (this sheep is my sheep, that sheep is your sheep)
whole -- (i guess you have no sheep, but i want to know that.)
integers -- (i want to compare my sheep to your sheep) [ways to denote a context of more and less]
rational numbers -- spaces between whole objects!
real numbers -- (skipping irrational for a moment);
a thing that can be counted or measured or described.
may give positive or negative values, but simply means a thing that can be measured.
sqrt(2) gives us issues. pi gives us issues.
this causes a subset of REAL numbers that cannot be written as fractions, and therefore not as decimals
imaginary numbers -- so what does it mean if a number is not 'real'?
let's do some ordering of our numbers...