- Announcements:
- Return HW4 (key); graded 16, 19, 21, and 24.
- Problems due today: Section 3.2, pp. 156-161, Mindscapes #6-8, 14, 15, 20
- We have an exam Wednesday, through our "Infinity" unit. That means
we will cover four units on the exam:
- Fun and Games
- Estimation
- Number Systems
- Infinity
Questions on things in preparation for the exam?
- Where have you encountered infinity before in your lives?
- Questions on 3.2 problems?
- Section 3.4: stratosphere of infinities
- A set S is a collection of objects, called elements of the
set.
- A subset of set S is a collection of objects contained entirely
within S.
- Where have you used sets and subsets in real life (whether you
know it or not)?
- The Power set
- is the set of all subsets of a set.
- Power sets lead to bigger sets.
- Power sets lead to bigger sets even in the case of
infinite sets!
- Check 3.4 problems: #5, 6, 7, 8
- We'll do the demonstration that there's a larger infinity
than the natural numbers, based on the text (pp. 180-)
- A proof (following the idea of Dodge Ball) that there is an
infinite set too big to be contained in "Motel Infinity".
- Now: how many different sizes of infinity are there?
- The Fourth Dimension:
- What thoughts and questions do you have about the fourth
dimension? What is the "fourth dimension"? Where have you
already encountered the fourth dimension?
- Sweeping out additional dimensions ("inked points")
- point (imprisoned!)
- point -> line (imprisoned by two points, each on one
side)
- line -> plane (imprisoned by a circle)
- plane -> three-space (imprisoned by a sphere)
- three-space -> the fourth dimension!
- Slicing and dicing: Problems II.6, II.7
- What if there were creatures confined to two dimensions? How would
we mess with their heads?
- Safes aren't safe (p. 312)
- 3-D surgery (p. 311)
- 3-D rope tricks (p. 313)
- How might a cube dipped into two-space appear to creatures
stuck in two-space?
- Now: what if there are four dimensional creatures living with us?
How might they mess with our heads?
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