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- Logic
- Propositional calculus
- First-order logic
- Second-order arithmetic
- Second-order logic
- Set theory
- Fuzzy set
- Zermelo–Fraenkel set theory
- Descriptive set theory
- Empty set
- Algebra of sets
- Axiom of choice
- Axiom of dependent choice
- Axiom of countable choice
- Well-ordering theorem
- Axiom of extensionality
- Axiom of regularity
- Axiom schema of specification
- Axiom of pairing
- Axiom of union
- Axiom of infinity
- Axiom of power set
- Axiom schema of replacement
- Math Foundations
- Addition
- Subtraction
- Multiplication
- Division (mathematics)
- Exponentiation
- Square root
- Nth root
- Negative and non-negative numbers
- Natural number
- Integer
- Rational number
- Real number
- Complex number
- Cube root
- Nested radical
- Imaginary number
- Quaternion
- Octonion
- Sedenion
- Hypercomplex number
- Tessarine
- Multicomplex number
- Split-complex number
- Imaginary unit