Arithmetic
The branch of mathematics dealing with Integers or, more generally, numerical computation. Arithmetical operations include Addition, Congruence calculation, Division, Factorization,Multiplication, Power computation, Root extraction, and Subtraction.
The Fundamental Theorem of Arithmetic, also called the Unique Factorization Theorem, states that anyPositive Integer can be represented in exactly one way as a Product of Primes.
The Löwenheim-Skolem Theorem, which is a fundamental result in Model Theory,establishes the existence of ``nonstandard'' models of arithmetic.
See also Algebra, Calculus, Fundamental Theorem of Arithmetic, Group Theory, Higher Arithmetic,Linear Algebra, Löwenheim-Skolem Theorem, Model Theory, NumberTheory, Trigonometry
References
Karpinski, L. C. The History of Arithmetic. Chicago, IL: Rand, McNally, & Co., 1925. Maxfield, J. E. and Maxfield, M. W. Abstract Algebra and Solution by Radicals. Philadelphia, PA: Saunders, 1992. Thompson, J. E. Arithmetic for the Practical Man. New York: Van Nostrand Reinhold, 1973.
Arithmetic
- Euclid's Postulates
- Euclid's Principle
- Euclid's Theorems
- Eudoxus's Kampyle
- Euler Angles
- Euler-Bernoulli Triangle
- Euler Brick
- Euler Chain
- Euler Characteristic
- Euler Constant
- Euler Curvature Formula
- Euler Differential Equation
- Euler Equation
- Euler Formula
- Euler Four-Square Identity
- Euler Graph
- Eulerian Circuit
- Eulerian Cycle
- Eulerian Integral of the First Kind
- Eulerian Integral of the Second Kind
- Eulerian Number
- Eulerian Trail
- Euler Identity
- Euler Integral
- Euler-Jacobi Pseudoprime