Definition:Arithmetic

Definition

Arithmetic is the branch of mathematics which concerns the manipulation of numbers, using the operations addition, subtraction, multiplication and division, and the taking of powers.

Also see

• Definition:Number Theory, sometimes referred to as the higher arithmetic.

• Results about arithmetic can be found here.

Linguistic Note

The word arithmetic, when used as a noun, is pronounced with the stress on the second syllable: a-rith-me-tic.

Its adjectival form, on the other hand, places the stress on the first and third syllables: a-rith-met-ic.

To avoid confusion between the noun and adjective, the adjectival form arithmetical is often used, being pronounced a-rith-met-ic-al.

Sources

• 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S 1.1$: Constants and variables
• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.1$. Number Systems
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): arithmetic: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): arithmetic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): arithmetic
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): arithmetic
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): arithmetic