Maths

Glossary

Number Systems

• ℕ - The set of natural numbers. No zero. No negatives. Subtraction and division aren't always possible. ℕ = {1, 2, 3, ...}.
• ℤ - The set of integers. Subtraction is always possible. ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}
• ℚ - The set of rational numbers (Quotient). Fractions. Division is always possible. ℚ is a field.
• ℝ - The set of real numbers. Includes irrational and transcendental numbers. √(2), π, e. ℝ⁺ for positive reals. ℝ is an extension of ℚ to a larger field.
• ℂ - The set of complex numbers. i²=-1

Algebraic Structures

• Set - A collection of elements.
• Group - A set with a binary operation. The operation must be associative. If the operation is also commutative then it is an Abelian group. [TODO]: Get Axioms.
• Field -