Proof, logic and sets
Quantifiers, proof techniques, functions, and how to compare the sizes of infinite sets.
1 lesson open · 9 planned
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Planned
In learning order. These are not pages yet.
- Reading ∀ and ∃, and why their order mattersIntro
- Negating statements with quantifiersIntro
- Proof by induction as a chain of dominoesIntro
- Injective, surjective, bijective functionsIntro
- Proof by contradiction: why √2 is irrationalIntro
- Equivalence relations and partitionsIntro
- Countable sets: listing every rational numberIntro
- Hilbert's hotel and the arithmetic of infinityIntro
- Cantor's theorem: a power set is always biggerAdvanced undergrad
How it connects
Builds on none
Leads to Real analysis Abstract algebra Number theory Stochastic processes connection Arbitrage and risk-neutral pricing connection Probability connection
Subjects marked “connection” are linked by a related idea, not by a prerequisite.