A gallery or a tier of cells. (in a prison)

- american underworld dictionary - 1950

The range of a matrix A, noted range(A), is the set of all vectors y that can be obtained by multiplying A with a vector x so that y=Ax. It is thus the space spanned by the columns of A.

In general:

For any function f(x), the range is all the numbers that f(x) can possibly output.

Let's say that f(x) = 3x-15. Now, for any real number you can think of, there's an x value than we can plug into f(x) to get that number. So we say that the range of f(x) is all real numbers, or, in set notation, {f(x):f(x)R}.

For our second example, g(x) = 3/(x-1). Now, since the numerator of 3/(x-1) is positive, then there's no value for x-1, and therefore no value for x, that will make the function equal 0. So the range of g(x) is all real numbers save for 0: {g(x):g(x)!=0}. (In this case, g(x) being an element of the real numbers is implied.)

One more: h(x) = sqrt(x). Now, remember that putting any negative x into this function will return a nonreal answer, which would be a Bad Thing. Subsequently, there is no real x which, when put into h(x), will output a negative answer. The range of h(x), therefore, is all numbers greater than or equal to 0, or {h(x):h(x)>=0}.

Contrast domain.

The range of a function f:AB is B.

Normally the range of a function is not specified, and in that case the range is usually taken to be the codomain of the function. However, this is not always the case: if the range were always the codomain, then all functions would be, by definition, surjective. It is true that every function has an equivalent function, with the range restricted to the codomain, but the mathematical definition of 'range' is different from 'codomain'. It is also true that the range is always a superset of the codomain, by necessity.

Compare with domain and codomain.

also applied to musical instruments. Indicates the range of pitch which the instrument can produce. Generally stated in octaves.

In Python, the built-in function range(x) returns the list [0, 1, 2, ..., x-1]. The standard idiom for looping over some index (0 to x-1) is thus for i in range(x).

Actually, range is more versatile than that. range(start, end, skip) (with any numeric arguments, not just integers) returns a list of values beginning with start, incremented by skip each time, and ending on the last value before end. skip defaults to 1. If there is just one argument, it is taken to be end, and start=0.

It is often much better to use xrange, a built-in iterator type, an instance of which which returns the same values as an iteration over a range-generated list, but never generates in memory the entire (possibly very long) list of values. The arguments to the constructor are identical.

Range (?), v. t. [imp. & p. p. Ranged (?); p. pr. & vb. n. Ranging (?).] [OE. rengen, OF. rengier, F. ranger, OF. renc row, rank, F. rang; of German origin. See Rane, n.]

1.

To set in a row, or in rows; to place in a regular line or lines, or in ranks; to dispose in the proper order; to rank; as, to range soldiers in line.

Maccabeus ranged his army by hands. 2 Macc. xii. 20.

2.

To place (as a single individual) among others in a line, row, or order, as in the ranks of an army; -- usually, reflexively and figuratively, (in the sense) to espouse a cause, to join a party, etc.

It would be absurd in me to range myself on the side of the Duke of Bedford and the corresponding society. Burke.

3.

To separate into parts; to sift.

[Obs.]

Holland.

4.

To dispose in a classified or in systematic order; to arrange regularly; as, to range plants and animals in genera and species.

5.

To rove over or through; as, to range the fields.

Teach him to range the ditch, and force the brake. Gay.

6.

To sail or pass in a direction parallel to or near; as, to range the coast.

⇒ Compare the last two senses (5 and 6) with the French ranger une cote.

7. Biol.

To be native to, or to live in; to frequent.

Range, v. i.

1.

To rove at large; to wander without restraint or direction; to roam.

Like a ranging spaniel that barks at every bird he sees. Burton.

2.

To have range; to change or differ within limits; to be capable of projecting, or to admit of being projected, especially as to horizontal distance; as, the temperature ranged through seventy degrees Fahrenheit; the gun ranges three miles; the shot ranged four miles.

3.

To be placed in order; to be ranked; to admit of arrangement or classification; to rank.

And range with humble livers in content. Shak.

4.

To have a certain direction; to correspond in direction; to be or keep in a corresponding line; to trend or run; -- often followed by with; as, the front of a house ranges with the street; to range along the coast.

Which way the forests range. Dryden.

5. Biol.

To be native to, or live in, a certain district or region; as, the peba ranges from Texas to Paraguay.

Syn. -- To rove; roam; ramble; wander; stroll.

Range, n. [From Range, v.: cf. F. rang'ee.]

1.

A series of things in a line; a row; a rank; as, a range of buildings; a range of mountains.

2.

An aggregate of individuals in one rank or degree; an order; a class.

The next range of beings above him are the immaterial intelligences. Sir M. Hale.

3.

The step of a ladder; a rung.

Clarendon.

4.

A kitchen grate.

[Obs.]

He was bid at his first coming to take off the range, and let down the cinders. L'Estrange.

5.

An extended cooking apparatus of cast iron, set in brickwork, and affording conveniences for various ways cooking; also, a kind of cooking stove.

6.

A bolting sieve to sift meal.

[Obs. or Prov. Eng.]

7.

A wandering or roving; a going to and fro; an excursion; a ramble; an expedition.

He may take a range all the world over. South.

8.

That which may be ranged over; place or room for excursion; especially, a region of country in which cattle or sheep may wander and pasture.

9.

Extent or space taken in by anything excursive; compass or extent of excursion; reach; scope; discursive; as, the range of one's voice, or authority.

Far as creation's ample range extends. Pope.

The range and compass of Hammond's knowledge filled the whole circle of the arts. Bp. Fell.

A man has not enough range of thought. Addison.

10. Biol.

The region within which a plant or animal naturally lives.

11. Gun. (a)

The horizontal distance to which a shot or other projectile is carried.

(b)

Sometimes, less properly, the trajectory of a shot or projectile.

(c)

A place where shooting, as with cannons or rifles, is practiced.

12.

In the public land system of the United States, a row or line of townships lying between two succession meridian lines six miles apart.

⇒ The meridians included in each great survey are numbered in order east and west from the "principal meridian" of that survey, and the townships in the range are numbered north and south from the "base line," which runs east and west; as, township No. 6, N., range 7, W., from the fifth principal meridian.

13. Naut.

See Range of cable, below.

Range of accommodation Optics, the distance between the near point and the far point of distinct vision, -- usually measured and designated by the strength of the lens which if added to the refracting media of the eye would cause the rays from the near point to appear as if they came from the far point. -- Range finder Gunnery, an instrument, or apparatus, variously constructed, for ascertaining the distance of an inaccessible object, -- used to determine what elevation must be given to a gun in order to hit the object; a position finder. -- Range of cable Naut., a certain length of slack cable ranged along the deck preparatory to letting go the anchor. -- Range work Masonry, masonry of squared stones laid in courses each of which is of even height throughout the length of the wall; -- distinguished from broken range work, which consists of squared stones laid in courses not continuously of even height. -- To get the range of (an object) Gun., to find the angle at which the piece must be raised to reach (the object) without carrying beyond.