Revision as of 00:05, 17 February 2017

Glossary

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

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.
Field -

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 * 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 - 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