THE COMPOUND // FIELD NOTES // WEEK 31
Counting, sets, and log equations
Field Book
Lessons 116 to 119
Method
Paper first, every step
The counting principle multiplies decisions. The Compound counts everything twice anyway, but once is mathematically sufficient.
What you have to be able to do
- Count arrangements with the counting principle and permutations
- Read and write set builder notation
- Solve logarithmic equations and the remaining absolute value inequalities
The procedures
Counting and probabilityField Book Lesson 116
- Multiply the options at each decision: that is the counting principle.
- Permutations count ordered arrangements: n factorial fills n slots. Independent events multiply their probabilities.
SetsField Book Lesson 117
- A set is a collection of elements, listed or described.
- Set builder notation describes membership: the x such that a condition holds.
Log equationsField Book Lesson 118
- If log A = log B on the same base, then A = B.
- Isolate a single log on each side before dropping them.
Absolute value with a centerField Book Lesson 119
- |x - C| measures distance from C.
- Under D means between C - D and C + D: the segment centered at C.
Worked: four in a row
- How many ways can four case files be shelved in order?
- 4 factorial = 4 times 3 times 2 times 1.
- 24 arrangements.
Terms on the record
| Term | Meaning |
|---|
| counting principle | multiply the number of options at each decision |
| permutation | an ordered arrangement of items |
| set builder notation | describing a set by the condition its members satisfy |