The Interval Debate

1) A set is just a collection of things. Consider these two sets:

The set of all ARHS classrooms numbered in the 300s
The set of all ARHS classrooms

Which set has more members? How can you be sure when you haven't actually counted the rooms?

2) You can also have sets which are collections of numbers. Here are some examples:

The set of all odd integers between 0 and 250
The set of all numbers between 0 and 100
The set of all numbers between 0 and 1

The last two sets are known as intervals, because they include the whole smear of the number line from the beginning point to the endpoint.

Here's the big question: Which interval includes more numbers-the interval from 0 to 1 or the interval from 0 to 100? Answer very carefully. Remember that I am asking you about all of the numbers in the interval-not just the whole numbers.

3) Question 2 has two different believable answers. What are they?

4) How is question 1 related to question 2?