Order of magnitude - Isou (English spelling)

Japanese: 位数 - いすう(英語表記)order
Order of magnitude - Isou (English spelling)
In mathematics, many objects, including symbols expressed as natural numbers, are called orders. For example, there are the following: (1) When group G is a finite set (finite group), if the number of elements of G is n , then n is called the order of G. (2) For an element a of group G , the smallest positive integer m for which a m = e ( e is the identity element of group G ) is called the order of a . For example, if ω is the m- th root of 1, then the smallest positive integer m for which ω m = 1 is the order of ω. (3) The maximum number of intersections between an algebraic curve C and a line l (obtained by moving l in various ways) is sometimes called an order. (4) If z = a is a pole of a complex function f ( z ), and the principal part of the expansion of f ( z ) into a Laurent series begins with the term ( z - a ) - n , then a is said to be the nth (order) pole. Also, n is called the order of a . Similarly, when f ( a ) = 0 and the Taylor expansion at a begins with the term ( z - a ) n , the order of the zero point a of f ( z ) is called n .

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:
数学では,自然数で表わされる標識について,位数と名づけられる対象が多い。たとえば次のような例がある。 (1) 群 G が有限集合 (有限群) であるとき,G の元の個数が n であれば,この nG の位数という。 (2) 群 G の1つの元 a に対し,ame ( e は群 G の単位元) となる最小の正整数 ma の位数という。たとえば,ω を1の m 乗根とすると,ωm=1 となるような最小の正の整数 m は,ω の位数である。 (3) 代数曲線 C と直線 l との交点の個数 ( l をいろいろと動かして得られる) の最大数を位数ということがある。 (4) za が複素関数 f(z) の極であって,f(z) をローラン級数に展開した主要部が (za)-n の項から始まるとき,an 位 (次) の極であるという。また na の位数という。同様に f(a)=0 で,a でのテイラー展開が (za)n の項から始まるとき,f(z) の零点 a の位数を n という。

出典 ブリタニカ国際大百科事典 小項目事典ブリタニカ国際大百科事典 小項目事典について 情報

<<:  Izu Oshima (English name)

>>:  Gastropancreatic correlation - Isuisoukan

Recommend

Unfair labor practice

Unfair labor practices are actions by employers t...

Industrial Classification - Sangyōbunrui

This is a statistical classification of various in...

Atmospheric refraction

In astronomical observations, the position of a ce...

Müller, Herta

Born August 17, 1953. Nitskidol is a German author...

Anonymous

...the language of the Vietnamese people who live...

O-araori

…Kudaka Island, which has a deep connection with ...

Homecoming - Kisei

[1] [noun] To return to one's hometown to chec...

Sijilmāsa (English spelling)

...Several oasis routes ran through the Sahara be...

Joban Line - Joban Line

The name of the East Japan Railway Company (JR Ea...

Thunder Beast - Raiju

〘Noun〙 An imaginary monster. It is said to fall to...

Nanbu Reconstruction (English)

A series of political, economic, and social measur...

Irikiin - Irikiin

The name of the region in the Middle Ages in Satsu...

Dynamical system - Rikigakukei (English spelling) dynamical sysytem

A method of describing the state of an arbitrary p...

Kakake

…Rice immediately after harvest contains about 20...

Kisch, A.

…In 1700, he plotted a rebellion with the help of...