# Vocabulary Word

**Word:**finite

**Definition:**limited

## Sentences Containing 'finite'

The sea had jeeringly kept his finite body up, but drowned the infinite of his soul.

The first element of the name is "not" which means "to fish using a seine" and the last element is the finite form of "odde" meaning "headland".

Farrell extended Tate cohomology groups to the case of all groups "G" of finite virtual cohomological dimension.

Finite groups have virtual cohomological dimension 0, and in this case Farrell's cohomology groups are the same as those of Tate.

Just as the Fourier transform for an infinite interval is related to the Fourier series over a finite interval, so the Hankel transform over an infinite interval is related to the Fourier–Bessel series over a finite interval.
Domain of definition.

He believed that the Universe, while not infinite, could not be held as finite as it lacked any bounds within which it could be contained.

As light has a finite velocity, this theory also constrains the size of the directly observable Universe.

This leaves open the question as to whether the Universe is finite or infinite.

In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.

The set of possible output values may be finite or countably infinite.

SRFI 41 enables the expression of both finite and infinite sequences with extraordinary economy.

All finite-dimensional statistical manifolds can be understood in this way.

Let formula_8 be a finite set of events determined by these variables.

We can also state the "Symmetric Algorithmic Lovász Local Lemma":
Let formula_40 be a finite set of mutually independent random variables and formula_4 be a finite set of events determined by these variables as before.

But when there is some sort of short-distance regulator on space time, the monopoles have a finite mass.

We may as well assume that the tree has no finite branches, as finite branches can be "unravelled" so make no difference.

The base ring "R" is taken to be the finite field formula_2.

A curve "C" has at most a finite number of singular points.

In mathematics, a topological space is feebly compact if every locally finite cover by nonempty open sets is finite.

Universal hashing can be defined as a mapping from a finite set "A" with size "a" to a finite set "B" with size "b".

The construction of MMH works in the finite field formula_24 for some prime integer formula_23.

Every finite extension of a finite field is a cyclic extension.

This finite volume is denoted by formula_1 and its bounding surface formula_2.

In particular, a finitely generated group with property FA has finite abelianization.

Indeed, any subgroup of finite index in a T-group has property FA.

In combinatorics, enumeration means counting, i.e., determining the exact number of elements of finite sets, usually grouped into infinite families, such as the family of sets each consisting of all permutations of some finite set.

In set theory, the notion of enumeration has a broader sense, and does not require the set being enumerated to be finite.

The name derives from this bijection (one-to-one correspondence) between the set of non-negative integers and the set of finite strings using a finite set of symbols (the "digits").

Based on his black-hole thermodynamics work, Bekenstein also demonstrated the Bekenstein bound: there is a maximum to the amount of information that can potentially be stored in a given finite region of space which has a finite amount of energy (which is similar to the holographic principle).

(locally finite implies point finite)
Refinement.

That is, we have the estimate
for all formula_4 for which the right-hand side is finite.

The Big Bang cosmology replaced this model (expanding, finite, and inhomogeneous universe).

The last element "-fjorden" (the finite form of fjord) is a later addition.

In mathematics, in the realm of group theory, a group is said to be thin if there is a finite upper bound on the girth of the Cayley graph induced by any finite generating set.

A "thin" group is a group where the girth has an upper bound for all finite generating sets.

Natural numbers can be considered either as finite ordinals or finite cardinals.

Here consider them as finite cardinal numbers.

In ZFC, a set formula_77 is finite if and only if there is formula_214 such that formula_215: further, define formula_193 as this "n" for finite "A".

Let "M" be a "GK"-module of finite order "m".

In theoretical physics, thermal quantum field theory or finite temperature field theory (or, shorter,
thermal field theory) is a set of methods to calculate expectation values of physical observables of a quantum field theory at finite temperature.

This has been shown to be a useful tool
in studying the behavior of quantum field theories at finite temperature.

Methods capable of treating finite regions have been applied to stars and to atomic nuclei.

The theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups and finite automata.

If this is finite, then "x" is said to be of finite order, otherwise it is of infinite order.

A semigroup is said to be periodic if all of its elements are of finite order.

If it is finite and nonempty, then it must contain at least one idempotent.

More can often be said when the order is finite.

For more on the structure of finite semigroups, see Krohn–Rhodes theory.

The term is used in English in 1908 in Harold Hinton's "Theory of Groups of Finite Order".

His 1928 paper "Über die endlichen Gruppen ohne das Gesetz der eindeutigen Umkehrbarkeit" ("On finite groups without the rule of unique invertibility") determined the structure of finite simple semigroups and showed that the minimal ideal (or Green's relations J-class) of a finite semigroup is simple.

# More Vocab Words

::: solstice - point or time at which the sun is farthest from the equator::: peccadillo - slight offense or fault; CF. sin

::: mnemonic - pertaining to memory; assisting the memory; N: device, such as as formula or rhyme, used as a mnemonic aid

::: surveillance - close observation of a person (esp. one under suspicion); watching; guarding

::: forensic - suitable to debate or courts of law; of or used in legal proceedings and the tracking of criminals; Ex. forensic science/medicine

::: glean - gather leavings; gather grain left behind by reapers; gather bit by bit (facts or information) often with difficulty

::: desiccate - dry up

::: fickle - changeable (in affections or friendship); faithless

::: unceremonious - not done politely without due formalities

::: barrage - barrier laid down by artillery fire; overwhelming profusion; large number of questions or statements; Ex. a barrage of criticism