# Numbers

### フレーズと例文

### large numbers (多数)

subspecies, varieties or ecotypes in large numbers.

They began to arrive in large numbers in the 1860s.

Other ancient sources give similarly large numbers.

### real numbers (実数)

This is the Archimedean property of real numbers.

In other words, the real numbers are not countable.

Rounding real numbers to integers is an example.

### small numbers (少数)

There are also small numbers of other minority groups.

One deals with small numbers, often called subitizing.

Wintering wildfowl include small numbers of whooper swan.

### complex numbers (複素数)

In these cases complex numbers are written as or .

This leads to the polar form of complex numbers.

Almost all real and complex numbers are transcendental.

### natural numbers

the set of natural numbers N = {0, 1, 2, 3, ...}.

First, place the natural numbers along the top row.

An illustrative example is sets picked from the natural numbers.

### increasing numbers

Similarly, the east-west routes use increasing numbers from north to south.

First Pakistani migrants came in the 1970s, with increasing numbers in the 1990s.

That same afternoon and evening, she encountered increasing numbers of wounded soldiers.

### significant numbers (かなりの数)

Leopards are present in significant numbers.

There are also significant numbers of Christians, Muslims.

Navarre and Catalonia also registered significant numbers.

### musical numbers

Herbert Ross choreographed the musical numbers.

List of acts, scenes and musical numbers.

Rare for the duo, it's a straight comedy with no musical numbers.

### passenger numbers

Eurostar passenger numbers continued to increase.

Eurostar's passenger numbers initially failed to meet predictions.

Within a year of launch, annual passenger numbers reached 17 million.

### numbers of people

Daily more than 1000 numbers of people visiting this place.

Escalators have the capacity to move large numbers of people.

Spamigation Spamigation is mass litigation conducted to intimidate large numbers of people.

### serial numbers (シリアルナンバー)

One of the guns had its serial numbers removed.

The serial numbers of the prototypes were "101" to "106".

SWCC imprinted all of their movements with serial numbers.

### phone numbers (電話番号)

Business plans include 2 phone numbers as standard.

in phone numbers), acronyms, arrows and many others.

Ribbit Mobile worked with users’ existing phone numbers.

### great numbers (素晴らしい数)

He has led great numbers of you astray.

It's collected for the aquarium trade, but not in great numbers.

They were however found in great numbers in the northern regions of Nandi.

### smaller numbers

Hindus are exist in comparatively smaller numbers.

### rational numbers (有理数)

), which is often the field of the rational numbers.

The set of rational numbers is not complete.

First, formula_78 is considered for rational numbers "y" only.

### telephone numbers

Over 90% of Taylors Lakes telephone numbers begin with "9390".

There are no area codes in Greenland, and all telephone numbers have 6 digits.

New York Telephone gave some 718 telephone numbers a head start for service by several days.

### larger numbers

Colonists now began purchasing slaves in larger numbers.

French started to immigrate in larger numbers after 1763.

Another deals with larger numbers in an approximate fashion.

### prime numbers

It is proved that there are infinitely many prime numbers.

That is, where ranges over the prime numbers less than or equal to .

This property does not imply that "a" or "b" are themselves prime numbers.

### greater numbers

Antony and Cleopatra had greater numbers of troops (i.e.

With much greater numbers and heavier weapons, the British Army suppressed the Rising.

With greater numbers came more diversity: Black and Hispanic student enrollment increased threefold.

### limited numbers

Designated MG 18 TuF (), it was issued in limited numbers in late World War I.

A 19" rack-mount version of both machines were also available in limited numbers.

As it was sold in limited numbers, the rear-engine Corsair remained in production.

### whose numbers

The Muslims, whose numbers he puts at 17,000, are "new Philistines".

The text is divided according to the Ammonian Sections, whose numbers are given at the margin.

The brightest illumination falls on the huddled victims to the left, whose numbers include a monk or friar in prayer.

### high numbers

Such high numbers from a state school are relatively rare.

TTC16 is found in high numbers in the testis, followed by the lung, pituitary gland, and tonsil.

Elephants tend to have high numbers of parasites, particularly nematodes, compared to other herbivores.

### population numbers

El Salvador's population numbers 6.1 million.

The permanent population numbers about 95,900 (2018 est.

The population numbers approximately 3000.

### huge numbers (膨大な数)

The Nairs had lost huge numbers of men in battles.

Commercially, huge numbers of cacti are produced annually.

They aggregate together in huge numbers.

### train numbers

It is operated with 22985/22986 train numbers on a weekly basis.

It is operated with 19667/19668 train numbers on a weekly basis.

It is currently being operated with 19317/19318 train numbers on weekly basis.

### route numbers

However, on May 25, 1927, several route numbers were revised, including Highways 5 and 6.

Though capable of displaying destination signs, they were not fitted to show route numbers.

As part of this change, trams would no longer display route numbers on their dot matrix destination screens.

### numbers are given

Page numbers are given in parentheses.

Individual canto numbers are given in bold for ease of reference.

The values of the first 20 Bernoulli numbers are given in the adjacent table.

### student numbers (学生数)

As the First World War approached, student numbers declined.

Boosting student numbers was, he said, his immediate priority.

The school closed again due to low student numbers in 1925, but reopened in 1931.

### superior numbers (優れた数)

Despite Grant's superior numbers, he had manpower challenges.

The Confederates withdrew under the pressure of superior numbers.

Villars, with superior numbers, was able to keep Eugene guessing as to his true intent.

### low numbers

Matthews claimed he had his best overall season despite the low numbers.

Hill End Primary School closed in 2006, due to very low numbers of enrolments.

Wild tigers, Eld's deer, wild water buffaloes and hog deer are at critically low numbers.

### equal numbers

The audience choice award went to Israfil and Yellow, which received equal numbers of votes.

Another problem of loss of significance occurs when two nearly equal numbers are subtracted.

Then Simonyi's result shows that there is a "t"-split with equal numbers of each real colour.

### different numbers

70 trios may be shown as having different numbers, if any.

Millers Fall and Sargent used different numbers to refer to the same planes.

"L. glaucus" belongs to a group that can be divided into different numbers of species.

### growing numbers

There were growing numbers of fights between whites and Indians.

The growing numbers of the community contributed to the monks' primary apostolate, retreat work.

To accommodate these growing numbers, the site at Jean Drapeau Park was expanded to a 42,500-person capacity.

### odd numbers (奇数)

Where marks are numbered red marks have even numbers and green marks have odd numbers.

This provides a very close match to justly tuned ratios consisting only of odd numbers.

The southern tip of the street (odd numbers till 9) faces the agreeable Jan Kochanowski Park.

### vast numbers (膨大な数)

The southern Plains Indians acquired vast numbers of horses.

It was produced in vast numbers; by August 1941 well over 6,000,000 had been manufactured.

Lemmings do migrate, and in vast numbers sometimes, but the deliberate march into the is false.

### numbers during

He recorded similar numbers during the 1953–1954 season.

Arab immigration to the United States began in sizable numbers during the 1880s.

Immigrants from Greece first started to settle in Baltimore in large numbers during the 1890s.

### even numbers

Almost all natural fatty acids, therefore, have even numbers of carbon atoms.

Where marks are numbered red marks have even numbers and green marks have odd numbers.

According to Davis, "Its great triumph was to prove that the sum of two even numbers is even".

### higher numbers

Typically, this has meant that rolling higher numbers is better.

Running PCMark produces a score with higher numbers indicating better performance.

These higher numbers would be the focus of much of the controversy in the issue to come.

### numbers between

All numbers between 10 and 20 are formed regularly (e.g.

Records show he recorded about 350 numbers between 1906 and 1917.

The net effect was to swap the numbers between roads on opposing ends of the state.

### quantum numbers

electrons in an atom) are described by a set of quantum numbers.

functions as real combinations of spherical harmonics (where and are quantum numbers).

These quantum numbers include the three that define orbitals, as well as , or spin quantum number.

### sufficient numbers

Street lights also in sufficient numbers for providing good lighting.

They are better than paid workers, and can be had in sufficient numbers."

He lacked sufficient numbers to defend the settlement, and he evacuated and abandoned .

### production numbers

The production numbers involved 84 skaters under dance director Henry Losee.

The Pellicano remained a popular aircraft locally though production numbers are uncertain.

American GA aircraft production numbers declined down from 18,000 in 1978 to 954 in 1993, an all-time low.

### dance numbers

A series of other short song and dance numbers presume.

She would have four dance numbers choreographed by herself and takes credit as the creative director.

They perform his showband era hits, dance numbers, nationalist songs, modern contemporary songs and concert hits.

### numbers increased

All day classes were consolidated here and pupil numbers increased rapidly.

Despite tough economic times, membership numbers increased and the Club's notoriety grew.

From 17,108 blacks in Kansas in 1870, the numbers increased to 43,107 in 1880 and 52,003 by 1900.

### substantial numbers

substantial numbers of electrons and holes recombine at the junction).

In North Carolina, bobcats ("Lynx rufus") consumed substantial numbers of hispid cotton rats.

Neither species was discovered in substantial numbers near the Falklands until the late 1980s.

### random numbers

They are used for generating random numbers and are commonly used in tabletop games.

Dice can be used to generate random numbers for use in passwords and cryptography applications.

'ACE' also references the fact that instead of dice, cards can be used to generate random numbers.

### visitor numbers

"Ice Age art" attracted large visitor numbers and good reviews.

Due primarily to falling visitor numbers the centre was redeveloped between 2009 and 2011.

During Paul's tenure, visitor numbers increased from around 250,000 per annum, peaking at over 600,000.

### highest numbers

Pennsylvania has one of the highest numbers of school districts in the nation.

Pennsylvania has one of the highest numbers of school districts in the United States.

The highest numbers of multilingual speakers lived in the Auckland, Wellington, and Canterbury regions.

### numbers of students

Increasing numbers of students from Bangladesh are arriving to Britain since at least 2002.

The massive numbers of students in one space easily caused fights to start, insubordination and a disturbance of peace.

In his lectures and art classes, Hunt attracted large numbers of students, many of them from prominent Brahmin families.

### numbers such

as ordered lists of numbers such as "(t,x,y,z)".

Some of these methods may work with non-natural numbers (numbers such as and ).

There are numbers such as the cube root of 2 which are algebraic but not constructible.

### increased numbers

A 2018 study of CDC data connected temperature rise to increased numbers of suicides.

Recently, there has been increased numbers of Engineers and Medical Student from this region.

By the 1880s, railroads brought increased numbers of settlers and ended the pueblos' isolation.

### negative numbers

Chinese mathematicians were the first to use negative numbers.

The four steps are: The engine represents negative numbers as ten's complements.

It allows some of the edge weights to be negative numbers, but no negative-weight cycles may exist.

### numbers and letters

He instructed his followers to memorize his teachings on the significance of numbers and letters.

Events are given a code, made of numbers and letters, describing the type of event and classification of the athletes competing.

### such numbers

Stanley, Grose, Rosenzweig, and Tom Lewis rejected such numbers.

During exercises such numbers of soldiers would swell to over 250,000.

According to the OEIS it is the largest publicly available database of such numbers.

### numbers are not

In other words, the real numbers are not countable.

Southern African numbers are not decreasing.

In the UK these numbers are not displayed.

### model numbers (型番)

These systems have the letter "L" appended to their model numbers.

New model numbers were assigned to distinguish them as new versions.

Common model numbers for these batteries were NP-1, NP-1A and NP-1B.

### pupil numbers (生徒数)

The village school closed because of falling pupil numbers.

By 1935, pupil numbers had reached 288.

All day classes were consolidated here and pupil numbers increased rapidly.

### peaked at numbers

The singles peaked at numbers 4 and 2 respectively on the UK singles chart.

It peaked at numbers eight and 71 on the US "Billboard" Top Heatseekers and Alternative Albums record charts.

In Australia and New Zealand, the song peaked at numbers four and five respectively and received gold certifications.

### all numbers

Consider the set of all numbers "ua" + "vb", where "u" and "v" are any two integers.

There are two parts to the test: in the first, the targets are all numbers (1, 2, 3, etc.)

For neuter nouns, the nominative and accusative forms are always the same, in all numbers.

### numbers of women

There has been a rise in the numbers of women joining the combat PAF in recent years.

Due to the longstanding economic instability of many of these nations, increasing numbers of women have been forced to turn towards the sex industry there for work.

The term has been replaced by more neutral ones, as gender-specific job titles have fallen into disuse, and because many systems employ large numbers of women in the position.

### considerable numbers

There are considerable numbers of taxis, buses, and public transport trucks providing service in and around town.

Despite it being long out of production, considerable numbers of Alouette II were still in service at the start of the 21st century.

In the naval operations surrounding the battle, both sides lost considerable numbers of ships and aircraft, including the Japanese battleship .

### exit numbers

Exit signs north of the interchange with US 6 previously included both miletabs and exit numbers before being replaced in 2007.

Its route is similar to that of the Pacific Motorway and can be accessed directly via exit numbers 20 and 14 as well as by the Gateway Motorway.

In 2018, the exit numbers at the interchanges for I-295 (Exits 60A-B) and U.S. Route 206 (Exits 1A-B) were renumbered to Exits 1 A-B and Exits 1 C-D, respectively.

### ordinal numbers

The aleph numbers are indexed by ordinal numbers.

He defined the cardinal and ordinal numbers and their arithmetic.

Khmer ordinal numbers are formed by placing the word in front of a cardinal number.

### other numbers (他の数字)

Sometimes, other numbers are omitted: a 2 on its own or indicates , for example.

On the residue-number criticism, Wrinch extended her model to allow for other numbers of residues.

To form other groups, other numbers, and units of length, time or capacity can be used with sanga-.

### numbers in parentheses

LMS numbers in parentheses were not carried prior to withdrawal.

Note: The numbers in parentheses are the tier of football for that season.

LMS numbers in parentheses were not carried prior to rebuilding as G1 or withdrawal.

### numbers represent

In the table below, the blue numbers represent the lowest ratings and the red numbers represent the highest ratings.

### letters and numbers

The reader guesses what the letters and numbers are supposed to represent in actual words.

His projects, besides letters and numbers, included watches, doorknobs, checkers, chess and dice.

Braille (a writing system for the blind) uses either 6 or 8 tactile 'points' from which all letters and numbers are formed.

### numbers of troops

Antony and Cleopatra had greater numbers of troops (i.e.

Nevertheless East Tennessee supplied significant numbers of troops to the Federal army.

The armed forces have deployed significant numbers of troops to the African Union Mission in Somalia since c. 2007.

### card numbers

Social engineering aims to convince a user to disclose secrets such as passwords, card numbers, etc.

Journalist Saeed Shah travelled to Kasab's village and produced national identity card numbers of his parents.

People could stand to lose much more than their credit card numbers in a world controlled by IoT-enabled devices.