Archived · Quiz 2 has passed — practice stays open. The active checkpoint is Quiz 3 →
Formula chains
Short compressed notes per week — formula chains linked to full week notes and pattern atlas dissections.
Week 1 · Mathematics I
Sets, number systems & functions
ℕ⊆ℤ⊆ℚ⊆ℝ → sets → relations → function test (one output per input).
5 formulas4 concepts3 traps
Full week note Week at a glance
- Set vs element: — distinguish from ; state the universal set before complements.
- Operations: — union, intersection, difference, complement, and Cartesian product as membership filters.
- Relations: — domain, codomain, range; reflexive/symmetric/transitive checks on small finite sets.
- Functions: — every input in the domain maps to exactly one output; use the vertical-line test on graphs.
Formula chain
- 1Membershipx ∈ A
x is an element of set A
- 2SubsetB ⊆ A
every element of B is in A
- 3Union / intersectionA∪B, A∩B
OR vs AND on membership
- 4Power set size|𝒫(A)| = 2^|A|
counting subsets
- 5Function rulef: D→C, each d∈D has exactly one f(d)
vertical line test on graphs
Classify before you calculate
Read each prompt aloud. Name the pattern family before opening a solution.
- What membership question defines in one sentence?
- How do you test a graph for being a function?
- Membership checklist: List elements of a small universal set and two subsets.