define

Dictionary: de·fine (dĭ-fīn') pronunciation

v., -fined, -fin·ing, -fines.

v.tr.

1. To state the precise meaning of (a word or sense of a word, for example).
2. To describe the nature or basic qualities of; explain: define the properties of a new drug; a study that defines people according to their median incomes.
1. To delineate the outline or form of: gentle hills that were defined against the sky.
2. To specify distinctly: define the weapons to be used in limited warfare.
To give form or meaning to: "For him, a life is defined by action" (Jay Parini).

v.intr.
To make or write a definition.

[Middle English definen, diffinen, from Old French definir, diffiner, from Latin dēfīnīre, to limit, determine : dē-, intensive pref.; see de- + fīnis, boundary, limit.]

definability de·fin'a·bil'i·ty n.
definable de·fin'a·ble adj.
definably de·fin'a·bly adv.
definement de·fine'ment n.
definer de·fin'er n.

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Antonyms: define

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Definition: give description
Antonyms: confuse, distort, tangle, twist

v

Definition: outline
Antonyms: conceal, obscure

Word Tutor: define

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IN BRIEF: To explain the meaning of a word or phrase.

Accept no one's definition of your life; define yourself.

Wikipedia: Defined and undefined

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In mathematics, defined and undefined are used to explain whether or not expressions have meaningful, sensible, and unambiguous values. Whether an expression has a meaningful value depends on the context of the expression. For example the value of 4 − 5 is undefined if a positive integer result is required.

Sometimes an expression is not well defined but the degree of undefinedness can be qualified in a useful way. There may be more than one possible value, or extra information might help to determine the value for instance.

1 Arithmetic forms
2 Notation using ↓ and ↑
3 See also

Arithmetic forms

Undefined forms

The following expressions are undefined in all contexts^{[citation needed]}, but remarks in the analysis section may apply.

$\infty - \infty$
$(-1)^{\pm\infty}$
$\frac{\pm\infty}{\pm\infty}$

The following form is normally undefined

$\frac{x}{0}$ for x≠0, but see division by zero on the real projective line

Indeterminate forms

They are defined in some, but not all contexts, as described in sections of this article. They are also indeterminate forms, if they occur as the limit of an expression it may be possible to find the value of the limit using other means.

Expression	Context in which it is used
$\frac{0}{0}$	See division by zero.
$00$	zero to the zero power, analysis, and set theory
$\infty^0$	analysis and set theory
$1^\infty$	analysis and set theory
$0 \cdot \infty$	set theory, and measure theory
$\infty - \infty$	analysis
$\frac{\infty}{\infty}$	analysis

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 is the common way of treating probability theory in mathematics), measures are preserved under countable addition. Taking $\infty$ as countable, $0 \cdot \infty = \sum_{n=0}^{\infty} 0 = 0$ .

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" .

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