The Activity Sequence

1. Computing the Even Numbers in Two Ways

rationale | worksheet | findings

 Can the same thing be made using all the numbers once and also using every other number once?
2. Combining Negative and Positive Integers Investigating if there are more negative and positive whole numbers than just positive whole numbers.
3. Generating different infinite sequences Comparing the "sizes of infinite sequences".
4. Generating a sequence of all fractions between 0 and 1 Generating all the rational numbers between 0 and 1.
5. Generating a sequence of all rational numbers greater than 1

rationale | worksheet 4 | worksheet 5 | findings

 Investigating whether there are more numbers between 1 and infinity than between 0 and 1.
6. Combining Negative and Positive Rational Numbers Investigating whether all the rational numbers are countable.
7. An infinite sequence of rational numbers between any two numbers Investigating whether there are an infinite number of rational numbers between any two rational numbers.
8. Counting All Infinite Sequences

rationale | worksheet | findings

 Investigating whether one can make a sequence of all sequences.

 

Dealing with infinite guests Solving the classic Hotel Infinity problems.

title | why | what | why toontalk | activities | rationale 1 | activity 1 | findings 1 | rationale 4/5 | activity 4 | activity 5 | findings 4/5 | rationale 8 | activity 8 | findings 8 | conclusions