Section
Shared Foundations
Basic set theory, logic, and function concepts used across all mathematics
Core idea
This section contains foundational definitions from set theory and mathematical logic used throughout analysis and algebra.
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Sets and Set Operations
- Set
- Empty set
- Subset
- Proper subset
- Union
- Intersection
- Set difference
- Complement
- Symmetric difference
- Power set
- Cartesian product
- Ordered pair
- Indexed family of sets
- Partition
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Functions
- Function (map)
- Domain
- Codomain
- Image
- Preimage
- Graph of a function
- Restriction
- Composition
- Identity function
- Inverse function
- Injective function
- Surjective function
- Bijective function
- Sequence
- Support of a function
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Relations
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Order
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Number Systems
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Cardinality
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Operations
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Axioms and Principles
- ZFC axioms
- Axiom of Choice
- Mathematical induction
- Well-ordering principle
- Well-ordering theorem
- Zorn's lemma
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Uncategorized
- Every bounded infinite subset of R^k has a limit point
- Complex conjugate
- Complex numbers
- Composition of functions
- Contraction mapping
- Morphism
- Total order (linear order)
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Arithmetic constructions
Logical language and finite indexing
- First-order logic and inference rules
- Mathematical propositions
- Mathematical axioms
- Mathematical proofs
- Theorems, lemmas, and corollaries
- Finite sets
- Finite sums
- Finite products
- Telescoping sums
- Binomial coefficients
- Rising factorials
- Floor
- Ceiling
- Nearest integer