arithmetization

The mathematician's arithmetization of geometry was a major breakthrough.

Definition

1. Noun:
   • The process of expressing or representing something in terms of arithmetic: "Arithmetization" refers to the act or result of converting a concept, problem, or system into a form that uses the basic operations of arithmetic (addition, subtraction, multiplication, division) or numerical quantities. This is often used in mathematics, logic, and computer science to reduce complex ideas to calculable forms.

Usage Examples

• (Converting geometric concepts into arithmetic terms.)
• (The process of representing logical statements with arithmetic.)
• (Translating economic theories into numerical calculations.)

Advanced Usage

• "Arithmetization of analysis": A historical movement in mathematics to ground calculus and analysis on rigorous arithmetic foundations, avoiding geometric intuition.
  • The arithmetization of analysis, led by mathematicians like Weierstrass and Dedekind, replaced vague geometric concepts with precise arithmetic definitions. (Establishing a numerical basis for calculus.)

Variants and Related Words

• Arithmetize (verb): to convert into arithmetic form.

  • The researcher sought to arithmetize the logical system for easier verification. (To express in arithmetic terms.)

• Arithmetic (noun/adjective): the branch of mathematics dealing with numbers and basic operations; relating to numbers.

  • Simple arithmetic is essential for everyday calculations. (The basic numerical operations.)

Synonyms

• Numerical representation: the expression of something using numbers.
• Quantification: the act of measuring or expressing as a quantity.

Phrasal Verbs

(No common phrasal verbs are associated with "arithmetization.")

Related Idioms

(No common idioms are associated with "arithmetization.")