Arabic
Bulgarian
Chinese
Croatian
Czech
Danish
Dutch
English
Estonian
Finnish
French
German
Greek
Hebrew
Hindi
Hungarian
Icelandic
Indonesian
Italian
Japanese
Korean
Latvian
Lithuanian
Malagasy
Norwegian
Persian
Polish
Portuguese
Romanian
Russian
Serbian
Slovak
Slovenian
Spanish
Swedish
Thai
Turkish
Vietnamese

Arabic
Bulgarian
Chinese
Croatian
Czech
Danish
Dutch
English
Estonian
Finnish
French
German
Greek
Hebrew
Hindi
Hungarian
Icelandic
Indonesian
Italian
Japanese
Korean
Latvian
Lithuanian
Malagasy
Norwegian
Persian
Polish
Portuguese
Romanian
Russian
Serbian
Slovak
Slovenian
Spanish
Swedish
Thai
Turkish
Vietnamese

definition of Wikipedia

Advertizing ▼

This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2012) |

In mathematics, **magnitude** is the "size" of a mathematical object, a property by which the object can be compared as larger or smaller than other objects of the same kind. More formally, an object's magnitude is an ordering (or ranking) of the class of objects to which it belongs.

## Contents |

The Greeks distinguished between several types of magnitude,^{[citation needed]} including:

- Positive fractions
- Line segments (ordered by length)
- Plane figures (ordered by area)
- Solids (ordered by volume)
- Angles (ordered by angular magnitude)

They proved that the first two could not be the same, or even isomorphic systems of magnitude.^{[citation needed]} They did not consider negative magnitudes to be meaningful, and *magnitude* is still chiefly used in contexts in which zero is either the lowest size or less than all possible sizes.

Main article: Absolute value

The magnitude of any number *x* is usually called its "absolute value" or "modulus", denoted by |*x*|.

The absolute value of a real number *r* is defined by:

- |
*r*| =*r*, if*r*≥ 0 - |
*r*| = -*r*, if*r*< 0.

It may be thought of as the number's distance from zero on the real number line. For example, the absolute value of both 7 and −7 is 7.

A complex number *z* may be viewed as the position of a point *P* in a 2-dimensional space, called the complex plane. The absolute value of *z* may be thought of as the distance of *P* from the origin of that space. The formula for the absolute value of *z* is similar to that for the Euclidean norm of a vector in a 2-dimensional Euclidean space:

where ℜ(*z*) and ℑ(*z*) are the respectively real part and imaginary part of *z*. For instance, the modulus of −3 + 4` i` is 5.

Main article: Euclidean norm

A Euclidean vector represents the position of a point *P* in a Euclidean space. Geometrically, it can be described as an arrow from the origin of the space (vector tail) to that point (vector tip). Mathematically, a vector **x** in an *n*-dimensional Euclidean space can be defined as an ordered list of *n* real numbers (the Cartesian coordinates of *P*): **x** = [*x*_{1}, *x*_{2}, ..., *x*_{n}]. Its **magnitude** or **length** is most commonly defined as its Euclidean norm (or Euclidean length):

For instance, in a 3-dimensional space, the magnitude of [4, 5, 6] is √(4^{2} + 5^{2} + 6^{2}) = √77 or about 8.775. This is equivalent to the square root of the dot product of the vector by itself:

The Euclidean norm of a vector is just a special case of Euclidean distance: the distance between its tail and its tip. Two similar notations are used for the Euclidean norm of a vector **x**:

The second notation is generally discouraged, because it is also used to denote the absolute value of scalars and the determinants of matrices.

Main article: Normed vector space

By definition, all Euclidean vectors have a magnitude (see above). However, the notion of magnitude cannot be applied to all kinds of vectors.

A function that maps objects to their magnitudes is called a norm. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space. In high mathematics, not all vector spaces are normed.

When comparing magnitudes, it is often helpful to use a logarithmic scale. Real-world examples include the loudness of a sound (decibel), the brightness of a star, or the Richter scale of earthquake intensity. Logarithmic magnitudes can be negative. It is usually not meaningful to simply add or subtract them.

Main article: Order of magnitude

In advanced mathematics, as well as colloquially in popular culture, especially geek culture, the phrase "order of magnitude" is used to denote a change in a numeric quantity, usually a measurement, by a factor of 10; that is, the moving of the decimal point in a number one way or the other, possibly with the addition of significant zeros.

Occasionally the phrase "half an order of magnitude" is also used, generally in more informal contexts. Sometimes, this is used to denote a 5 to 1 change, or alternatively 10^{1/2} to 1 (approximately 3.162 to 1).

sensagent's content

- definitions
- synonyms
- antonyms
- encyclopedia

Dictionary and translator for handheld

New : sensagent is now available on your handheld

Advertising ▼

Webmaster Solution

Alexandria

A windows (pop-into) of information (full-content of Sensagent) triggered by double-clicking any word on your webpage. Give contextual explanation and translation from your sites !

SensagentBox

With a SensagentBox, visitors to your site can access reliable information on over 5 million pages provided by Sensagent.com. Choose the design that fits your site.

Business solution

Improve your site content

Add new content to your site from Sensagent by XML.

Crawl products or adds

Get XML access to reach the best products.

Index images and define metadata

Get XML access to fix the meaning of your metadata.

Please, email us to describe your idea.

Lettris

Lettris is a curious tetris-clone game where all the bricks have the same square shape but different content. Each square carries a letter. To make squares disappear and save space for other squares you have to assemble English words (left, right, up, down) from the falling squares.

boggle

Boggle gives you 3 minutes to find as many words (3 letters or more) as you can in a grid of 16 letters. You can also try the grid of 16 letters. Letters must be adjacent and longer words score better. See if you can get into the grid Hall of Fame !

English dictionary

Main references

Most English definitions are provided by WordNet .

English thesaurus is mainly derived from The Integral Dictionary (TID).

English Encyclopedia is licensed by Wikipedia (GNU).

Copyrights

The wordgames anagrams, crossword, Lettris and Boggle are provided by Memodata.

The web service Alexandria is granted from Memodata for the Ebay search.

The SensagentBox are offered by sensAgent.

Translation

Change the target language to find translations.

Tips: browse the semantic fields (see From ideas to words) in two languages to learn more.

last searches on the dictionary :

WICC (AM) ·
Carl Legien ·
excitation ·
JANET PARSHALL ·
sun erniang ·
versity ·
Caro Dawes ·
SLOPPIEST ·
Z (album) ·
BUNKER ·

2908 online visitors

computed in 0.546s

I would like to report:

section :

a spelling or a grammatical mistake

an offensive content(racist, pornographic, injurious, etc.)

a copyright violation

an error

a missing statement

other

please precise: