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# characteristic

### Overview

This page has 6 definitions of characteristic in English and Interlingua (International Auxiliary Language Association). Characteristic is an adjective and noun. Examples of how to use characteristic in a sentence are shown. Also define these 17 related words and terms: distinguish, feature, distinguishing, mathematics, integer, logarithm, nautical, navigational, light, lighthouse, algebra, field, ring, natural number, multiplicative identity, additive identity, and characteristic.

## English

### Etymology

From Ancient Greek χαρακτηριστικός (kharaktēristikós), from χαρακτηρίζω (kharaktērízō, to designate by a characteristic mark), from χαρακτήρ (kharaktḗr, a mark, character).

### Pronunciation

characteristic (comparative more characteristic, superlative most characteristic)

1. Being a distinguishing feature of a person or thing.
• 1918, W. B. Maxwell, chapter 12, in The Mirror and the Lamp:
All this was extraordinarily distasteful to Churchill. It was ugly, gross. Never before had he felt such repulsion when the vicar displayed his characteristic bluntness or coarseness of speech. In the present connexion […] such talk had been distressingly out of place.

### Noun

characteristic (plural characteristics)

1. A distinguishing feature of a person or thing.
• ##### Distinguishing definition
2. (mathematics) The integer part of a logarithm.
• 1830, Solomon Pearson Miles, Thomas Sherwin, Mathematical Tables: Comprising Logarithms of Numbers, [] , page 69,
It is evident, moreover, that as the logarithms of numbers, which are tenfold, the one of the other, do not differ except in their characteristics, it is sufficient that the tables contain the fractional parts only of the logarithms.
• 1911, F. T. Swanwick, Elementary Trigonometry, Cambridge University Press, page 60,
As the sine and cosine are always proper fractions their logarithms are negative, i.e. have negative characteristics. When we are given an angle, it is impossible to say, from inspection of the angle, what the characteristic of the logarithm of its sine, cosine or tangent may be; so the characteristics have to be printed with the mantissae.
• 1961, Principles and Applications of Mathematics for Communications-Electronics, [U.S.] Department of the Army, page 69,
Similarly, the characteristic for .003 is −3, and the characteristic for .0003 is −4.
• ##### Integer definition
English Wikipedia has an article on:
Wikipedia
A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
• ##### Logarithm definition
For a number ${\displaystyle x}$ , the power to which a given base number must be raised in order to obtain ${\displaystyle x}$ . Written ${\displaystyle \log _{b}x}$ . For example, ${\displaystyle \log _{10}1000=3}$ because ${\displaystyle 10^{3}=1000}$ and ${\displaystyle \log _{2}16=4}$ because ${\displaystyle 2^{4}=16}$ .
3. (nautical) The distinguishing features of a navigational light on a lighthouse etc by which it can be identified (colour, pattern of flashes etc.).
• ##### Nautical definition
Relating to or involving ships or shipping or navigation or seamen.
4. (algebra, field theory, ring theory) For a given field or ring, a natural number that is either the smallest positive number n such that n instances of the multiplicative identity (1) summed together yield the additive identity (0) or, if no such number exists, the number 0.
The characteristic of a field, if non-zero, must be a prime number.
• 1962 [John Wiley & Sons], Nathan Jacobson, Lie Algebras, 1979, Dover, page 289,
In this chapter we study the problem of classifying the finite-dimensional simple Lie algebras over an arbitrary field of characteristic 0.
• 1992, Simeon Ivanov (translator), P. M. Gudivok, E. Ya. Pogorilyak, On Modular Representations of Finite Groups over Integral Domains, Simeon Ivanov (editor), Galois Theory, Rings, Algebraic Groups and Their Applications, American Mathematical Society, page 87,
Let R be a Noetherian factorial ring of characteristic p which is not a field.
• 1993, S. Warner, Topological Rings, Elsevier (North-Holland), page 424,
Traditionally, a complete, discretely valued field of characteristic zero, the maximal ideal of whose valuation ring is generated by the prime number p, has been called a p-adic field. In our terminology, the valuation ring of a p-adic field is a Cohen ring of characteristic zero whose residue field has characteristic p, and consequently a p-adic field is simply the quotient field of such a Cohen ring.
• ##### Algebra definition
A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols. (1 of 8 algebra definitions)
An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally denoted +). That is, x + 0 = 0 + x = x for any x in the structure.

#### Derived terms

• defining characteristic

#### Translations

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