ALGEBRAIC NUMBER Meaning and
Definition
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An algebraic number refers to a complex number that is a root of a polynomial equation with integer coefficients. In other words, it is a solution to an algebraic equation that can be expressed using arithmetic operations (addition, subtraction, multiplication, division) and taking roots (square roots, cube roots, etc.).
Algebraic numbers can be both real numbers and complex numbers, and they form a subset of the set of complex numbers. They can be classified further into two types: rational and irrational algebraic numbers.
Rational algebraic numbers are those that can be expressed as a fraction, where the numerator and denominator are integers. They include integers, fractions, and roots of integers. For example, 2, -3/5, and √9 (which equals 3) are rational algebraic numbers.
On the other hand, irrational algebraic numbers cannot be expressed as a fraction. They are typically expressed as the root of a polynomial equation. Examples of irrational algebraic numbers include √2, √3, and the golden ratio.
Algebraic numbers have several important properties. They can be added, subtracted, multiplied, and divided to produce other algebraic numbers. They can also be ordered and compared based on their numerical values. Furthermore, algebraic numbers can be approximated by rational numbers to any desired degree of accuracy, making them valuable in various mathematical applications and calculations.
Common Misspellings for ALGEBRAIC NUMBER
- zlgebraic number
- slgebraic number
- wlgebraic number
- qlgebraic number
- akgebraic number
- apgebraic number
- aogebraic number
- alfebraic number
- alvebraic number
- albebraic number
- alhebraic number
- alyebraic number
- altebraic number
- algwbraic number
- algsbraic number
- algdbraic number
- algrbraic number
- alg4braic number
- alg3braic number
Etymology of ALGEBRAIC NUMBER
The word "algebraic" comes from the Latin word "algebraicus", which originated from the Arabic term "al-jabr" meaning "reunion of broken parts". This term was introduced by the Persian mathematician Muhammad ibn Musa al-Khwarizmi in his work "Kitab al-Jabr wa al-Muqabala" in the 9th century. "Algebraicus" was later Latinized and used to describe a mathematical discipline known as "algebra".
The term "number" traces its roots back to the Latin word "numerus", which means "number" or "numeral". It entered the English language through the Old French word "nombre". The concept of numbers has been studied and developed by various ancient civilizations, including the Egyptians, Babylonians, Greeks, and Romans.
Similar spelling words for ALGEBRAIC NUMBER
