# Dictionary Definition

defined adj

1 clearly characterized or delimited; "lost in a
maze of words both defined and undefined"; "each child has clearly
defined duties" [ant: undefined]

2 showing clearly the outline or profile or
boundary; "hills defined against the evening sky"; "the setting sun
showed the outlined figure of a man standing on the hill" [syn:
outlined]

# User Contributed Dictionary

## English

### Pronunciation

- /dəˈfaɪnd/

### Verb

defined- past of define

### Adjective

- : Having extreme muscle separation as a result of low body fat.

### Related terms

# Extensive Definition

In mathematics, defined and
undefined are used to explain whether or not expressions have
meaningful, sensible, and unambiguous values. Not all branches of
mathematics come to the same conclusion.

## Examples and workarounds

The following expressions are undefined in all
contexts, but remarks in the
analysis section may apply.

The following are defined in some, but not all
contexts, as described in sections of this article.

### Zero to the zero power

The question of 0^0 may be the most common point on which branches of mathematics disagree. Here we note only two considerations, one from analysis and one from combinatorics, as an example of the way different approaches may yield different answers.In 1821, Cauchy
also listed 00 as undefined. The function 0x (for x>0) is
constantly 0, and the function x0 (for x>0) is constantly 1, so
there seems to be no natural value for 00. Indeed, for suitably
chosen continuous functions f and g with whose limit as x\to 0 is 0
(with f taking positive values), the limit

- \lim_ f(x)^

can be any nonnegative number, or infinity, or
fail to exist.

Modern textbooks often define 0^0=1. For example,
Ronald
Graham, Donald Knuth
and Oren
Patashnik argue in their book Concrete
mathematics:

### Analysis

In mathematical analysis the domain of a function is usually determined by the limit of the function, so as to make the function continuous. This definition makes all of the expressions undefined. In calculus, some of the expressions arise in intermediate calculations, where they are called indeterminate forms and dealt with using techniques such as L'Hôpital's rule.### Measure theory

In measure theory (which the common way of treating probability theory in mathematics), measures are preserved under countable addition. Taking \infty as countable, 0 \cdot \infty = \sum_^ 0 = 0.## Notation using ↓ and ↑

In computability theory, if f is a partial function on S and a is an element of S, then this is written as f(a)↓ and is read "f(a) is defined."If a is not in the domain of f, then f(a)↑ is
written and is read as "f(a) is undefined" .

## See also

defined in German: Unbestimmter
Ausdruck

# Synonyms, Antonyms and Related Words

absolute, certain, circumscribed, circumscript, clean-cut,
clear, clear as crystal,
clear as day, clear-cut, coherent, concrete, connected, consistent, conspicuous, crisp, crystal-clear, crystalline, definite, delimited, demarcated, detailed, determinate, determined, different, direct, distinct, distinguished, encircled, esoteric, especial, evident, exceptional, explicit, express, extraordinary, fixed, glaring, hedged about, in focus,
individual, inner, intimate, limpid, loud and clear, lucid, luminous, minute, noteworthy, obvious, particular, patent, pellucid, personal, perspicuous, plain, precise, private, prominent, pronounced, respective, set, several, simple, singular, solipsistic, special, specific, staring, stated, straightforward,
surrounded, translucent, transparent, transpicuous, unambiguous, unconfused, unequivocal, univocal, unmistakable, well-defined,
well-marked, well-pronounced, well-resolved