18 (number): Difference between revisions

← 17 18 19 →
← 10 11 12 13 14 15 16 17 18 19 → List of numbers; Integers; ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	eighteen
Ordinal	18th; (eighteenth)
Numeral system	octodecimal
Factorization	2 × 32
Divisors	1, 2, 3, 6, 9, 18
Greek numeral	ΙΗ´
Roman numeral	XVIII, xviii
Binary	100102
Ternary	2003
Senary	306
Octal	228
Duodecimal	1612
Hexadecimal	1216
Hebrew numeral	י"ח
Babylonian numeral	𒌋𒐜

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18 (eighteen) is the natural number following 17 and preceding 19. It is an even composite number.

Mathematics

18 is a semiperfect number^[1] and an abundant number. It is a largely composite number,^[2] as it has 6 divisors and no smaller number has more than 6 divisors. There are 18 one-sided pentominoes. In the classification of finite simple groups, there are 18 infinite families of groups.^[3]

In science

Chemistry

The 18-electron rule is a rule of thumb in transition metal chemistry for characterising and predicting the stability of metal complexes.

In religion and literature

The Hebrew word for "life" is חי (chai), which has a numerical value of 18. Consequently, the custom has arisen in Jewish circles to give donations and monetary gifts in multiples of 18 as an expression of blessing for long life.^[4]
In Judaism, in the Talmud; Pirkei Avot (5:25), Rabbi Yehudah ben Teime gives the age of 18 as the appropriate age to get married ("Ben shmonah esra lechupah", at eighteen years old to the Chupah (marriage canopy)). (See Coming of age, Age of majority).
Shemoneh Esrei (sh'MOH-nuh ES-ray) is a prayer that is the center of any Jewish religious service. Its name means "eighteen". The prayer is also known as the Amidah.
In Ancient Roman custom the number 18 can symbolise a blood relative.

As lucky or unlucky number

In Chinese tradition, 18 is pronounced 十八; shí bā and is considered a lucky number due to similarity with 實發; shì fā 'definitely get rich', 'to get rich for sure'.^[5]
According to applications of numerology in Judaism, the letters of the word chai ("living") add up to 18. Thus, 18 is considered a lucky number and many gifts for B'nai Mitzvot and weddings are in $18 increments.^[6]

Age 18

In most countries, 18 is the age of majority, in which a minor becomes a legal adult. It is also the voting age, marriageable age, drinking age and smoking age in most countries, though sometimes these ages are different than the age of majority. Many websites restrict adult content to visitors who claim to be at least 18 years old.

In the United States, 18 is the:
- Age for sexual consent in eleven states and under federal law.^[7]
- Minimum age to purchase firearms in thirty-eight states with the exception of handguns (21 under federal law).^[8]
- Marriageable age without parental consent except for Nebraska (19), Mississippi and Puerto Rico (21).
- The minimum age at which one can purchase, rent, or buy tickets to NC-17-rated films or buy video games with an Adults Only rating.
In the UK, 18 is the legal age to purchase a BBFC "18" rated film.
In Japan, 18 is the minimum age at which one can purchase, rent, or buy tickets to R18+ rated movies or buy video games with a Z rating, although 20 is their cultural age of adulthood.

In sports

In association football (soccer), "the 18" is a slang term for the penalty area.
In Nippon Professional Baseball (Japanese baseball), No.18 is known as the Ace number.

Notes

References

^ Sloane, N. J. A. (ed.). "Sequence A005835 (Pseudoperfect (or semiperfect) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
^ Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Wilson, Robert A. (2009). The finite simple groups. Graduate Texts in Mathematics. Vol. 251. Berlin, New York: Springer-Verlag. p. 3. doi:10.1007/978-1-84800-988-2. ISBN 978-1-84800-987-5. Zbl 1203.20012.
^ Benjaminson, Chani. "What is the reason for the custom to give money gifts in multiples of 18 -- 18, 36, 54, etc.?". Chabad.org. Archived from the original on 2007-12-27. Retrieved January 19, 2022.
^ 言必有「中」：「十八」「實發」人見人愛. 文匯報. Accessed 2015-01-12. Archived 2015-01-15.
^ "Chai, Its Meaning and Significance | Shiva, Jewish Mourning". www.shiva.com. Retrieved 2020-11-18.
^ "STATUTORY RAPE: A GUIDE TO STATE LAWS AND REPORTING REQUIREMENTS. SEXUAL INTERCOURSE WITH MINORS". Aspe. 23 November 2015.
^ "Minimum Age". Giffords.

[1] Sloane, N. J. A. (ed.). "Sequence A005835 (Pseudoperfect (or semiperfect) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.

[OEIS-A067128-2] Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[3] Wilson, Robert A. (2009). The finite simple groups. Graduate Texts in Mathematics. Vol. 251. Berlin, New York: Springer-Verlag. p. 3. doi:10.1007/978-1-84800-988-2. ISBN 978-1-84800-987-5. Zbl 1203.20012.

[4] Benjaminson, Chani. "What is the reason for the custom to give money gifts in multiples of 18 -- 18, 36, 54, etc.?". Chabad.org. Archived from the original on 2007-12-27. Retrieved January 19, 2022.

[5] 言必有「中」：「十八」「實發」人見人愛. 文匯報. Accessed 2015-01-12. Archived 2015-01-15.

[6] "Chai, Its Meaning and Significance | Shiva, Jewish Mourning". www.shiva.com. Retrieved 2020-11-18.

[7] "STATUTORY RAPE: A GUIDE TO STATE LAWS AND REPORTING REQUIREMENTS. SEXUAL INTERCOURSE WITH MINORS". Aspe. 23 November 2015.

[8] "Minimum Age". Giffords.

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@@ Line 1: / Line 1: @@
+{{redirect|XVIII|the Eighteen Visions album|XVIII (album){{!}}''XVIII'' (album)}}
-{{Redirect|Eighteen||18 (disambiguation)}}
-{{Multiple issues|
-{{example farm|date=March 2010}}
-{{confusing|date=February 2012}}
-}}
 {{Infobox number
 | number =  18
 | numeral = [[octodecimal]]
 | divisor = 1, 2, 3, 6, 9, 18
+|lang1=[[Hebrew numerals|Hebrew numeral]]|lang1 symbol=<span style="font-size:150%;">י"ח</span>|lang2=[[Babylonian cuneiform numerals|Babylonian numeral]]|lang2 symbol=𒌋𒐜}}
-}}
 {{wiktionary|eighteen}}
-'''18''' ('''eighteen''') is the [[natural number]] following [[17 (number)|17]] and preceding [[19 (number)|19]].
+'''18''' ('''eighteen''') is the [[natural number]] following [[17 (number)|17]] and preceding [[19 (number)|19]]. It is an even [[composite number]].
-In speech, the numbers 18 and 80 are sometimes confused. When carefully enunciated, they differ in which syllable is [[stress (linguistics)|stressed]]: 18 {{IPAc-en|eɪ|t|ˈ|t|iː|n}} vs 80 {{IPAc-en|ˈ|eɪ|t|i}}. However, in dates such as 1864, or when contrasting numbers in the teens, such as ''17, 18, 19,'' the stress shifts to the first syllable: 18 {{IPAc-en|ˈ|eɪ|t|t|iː|n}}. In some dialects, such as [[General American]], there is little confusion because the single ''t'' sound in 80 becomes a ''d''-like [[alveolar flap|flap]] {{IPA|[ɾ]}}, whereas the double ''t'' sound in 18 does not.
-==In mathematics==
+==Mathematics==
+is a [[semiperfect number]]<ref>{{Cite OEIS|A005835|Pseudoperfect (or semiperfect) numbers|access-date=2016-05-31}}</ref> and an [[abundant number]]. It is a [[largely composite number]],<ref name="OEIS-A067128">{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}</ref> as it has 6 [[divisor]]s and no smaller number has more than 6 divisors. There are 18 [[One-sided polyomino|one-sided]] [[pentomino]]es. In the [[classification of finite simple groups]], there are 18 infinite families of  groups.<ref>{{cite book | last=Wilson | first=Robert A. | authorlink = Robert Arnott Wilson | title=The finite simple groups | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=[[Graduate Texts in Mathematics]] | isbn=978-1-84800-987-5 | doi=10.1007/978-1-84800-988-2 | year=2009 | zbl=1203.20012 | volume=251 | page=3 }}</ref>
-Eighteen is a [[composite number]], its proper [[divisor]]s being [[1 (number)|1]], [[2 (number)|2]], [[3 (number)|3]], [[6 (number)|6]] and [[9 (number)|9]]. Three of these divisors (3, 6 and 9) add up to 18, hence 18 is a [[semiperfect number]]. Eighteen is the first inverted square-prime of the form p.q<sup>2</sup>.
-It is a [[heptagonal number]], and as the sum of the first three [[pentagonal number]]s, it is a [[pentagonal pyramidal number]]. It is also the sum of the [[totient function]] for the first seven integers. It is the sixth [[lucas number]].
-Eighteen is the second [[abundant number]]  with the [[aliquot sum]] of 21 (117% in abundance) in the  [[aliquot sequence]]  (18, [[21 (number)|21]], [[11 (number)|11]], [[1 (number)|1]], 0) thus being the first [[composite number]] in the 11-aliquot tree. Eighteen is the [[aliquot sum]] of only one number the square [[289 (number)|289]].
-In base 10 it is a [[Harshad number]].
-, aside from 0, is the only number that equals twice the sum of its decimal digits.
 ==In science==
+===Chemistry===
-*The [[atomic number]] of [[argon]]
-*The [[18-Electron rule|18-electron rule]] is a [[rule of thumb]] in [[transition metal]] [[chemistry]] for characterising and predicting the stability of [[Metal complex#Metal complexes|metal complexes]]
+* The [[18-Electron rule|18-electron rule]] is a [[rule of thumb]] in [[transition metal]] [[chemistry]] for characterising and predicting the stability of [[Metal complex#Metal complexes|metal complexes]].
-*The number of years in the [[Saros cycle]] of [[Eclipse cycle|eclipses]] of the sun and moon
 ==In religion and literature==
-*The [[Hebrew language|Hebrew]] word for "life" is חי (''[[Chai (symbol)|chai]]''), which has a [[gematria|numerical value]] of 18. Consequently, the custom has arisen in Jewish circles to give donations and monetary gifts in multiples of 18 as an expression of blessing for long life.
+* The [[Hebrew language|Hebrew]] word for "life" is {{Lang|he|חי}} (''[[Chai (symbol)|chai]]''), which has a [[gematria|numerical value]] of 18. Consequently, the custom has arisen in Jewish circles to give donations and monetary gifts in multiples of 18 as an expression of blessing for long life.<ref>{{Cite web|last=Benjaminson|first=Chani|title=What is the reason for the custom to give money gifts in multiples of 18 -- 18, 36, 54, etc.?|url=https://www.chabad.org/library/article_cdo/aid/484894/jewish/What-is-the-reason-giving-money-in-multiples-of-18.htm|url-status=live|access-date=January 19, 2022|website=Chabad.org|archive-url = https://web.archive.org/web/20071227215754/http://www.chabad.org/library/article_cdo/aid/484894/jewish/What-is-the-reason-giving-money-in-multiples-of-18.htm  |archive-date = 2007-12-27  }}</ref>
-*In [[Judaism]], in the [[Talmud]]; [[Pirkei Avot]] (5:25), Rabbi Yehudah ben Teime gives the age of 18 as the appropriate age to get married (''"Ben shmonah esra lechupah"'', at eighteen years old to the [[Chupah]] (marriage canopy)). (See [[Coming of age]], [[Age of majority]]).
+* In [[Judaism]], in the [[Talmud]]; [[Pirkei Avot]] (5:25), Rabbi Yehudah ben Teime gives the age of 18 as the appropriate age to get married (''"Ben shmonah esra lechupah"'', at eighteen years old to the [[Chupah]] (marriage canopy)). (See [[Coming of age]], [[Age of majority]]).
-*Shemoneh Esrei (sh'MOH-nuh ES-ray)
+* Shemoneh Esrei (sh'MOH-nuh ES-ray) is a prayer that is the center of any Jewish religious service. Its name means "eighteen". The prayer is also known as the [[Amidah]].
+* In [[Ancient Roman]] custom the number 18 can symbolise a [[blood relative]].
-Lit. eighteen. A prayer that is the center of any Jewish religious service. Also known as the Amidah. See Jewish Liturgy. jewfaq.org
-*In [[Ancient Roman]] custom the number 18 can symbolise a [[blood relative]].
-*[[Joseph Heller]]'s novel ''[[Catch-22]]'' was originally named ''Catch-18'' because of the Hebrew meaning of the number, but was amended to the published title to avoid confusion with another war novel, [[Mila 18]].<ref name="title">N James. ''The Early Composition History of Catch-22''. In Biographies of Books: The Compositional Histories of Notable American Writings, J Barbour, T Quirk (edi.) pp. 262-90. Columbia: [[University of Missouri Press]], 1996</ref>
-*There are 18 chapters in the [[Bhagavad Gita]], which is contained in the [[Mahabharata]], which has 18 books. The [[Kurukshetra War]] which the [[Indian epic poetry|epic]] depicts, is between 18 armies (11 on the [[Kuru (kingdom)|Kuru]] side, 7 on the [[Pandava]]).  The war itself also lasts for 18 days.
-*A shape looking like 18 in [[Eastern Arabic numerals|Arabic numbers]] is formed by the lines on the palm of the right hand.
 ==As lucky or unlucky number==
-* In [[Numbers in Chinese culture|Chinese tradition]], 18 pronounced 十八 (shí bā) and is a considered lucky number due to similarity with 實發 (shì fā) 'definitely get rich', 'to get rich for sure'.<ref>[http://paper.wenweipo.com/2014/02/19/ED1402190024.htm 言必有「中」：「十八」「實發」 人見人愛]. 文匯報. Accessed 2015-01-12.  [http://www.webcitation.org/6VaWKwys4 Archived] 2015-01-15.</ref>
+* In [[Numbers in Chinese culture|Chinese tradition]], 18 is pronounced {{Lang-zh|c=十八|p=shí bā|labels=no}} and is considered a lucky number due to similarity with {{Lang-zh|c=實發|p=shì fā|labels=no}} 'definitely get rich', 'to get rich for sure'.<ref>[http://paper.wenweipo.com/2014/02/19/ED1402190024.htm 言必有「中」：「十八」「實發」 人見人愛]. 文匯報. Accessed 2015-01-12. [https://web.archive.org/web/20150609062855/http://paper.wenweipo.com/2014/02/19/ED1402190024.htm Archived] 2015-01-15.</ref>
+*According to applications of [[Gematria|numerology in Judaism]], the letters of the word ''[[Chai (symbol)|chai]]'' ("living") add up to 18. Thus, 18 is considered a lucky number and many gifts for [[Bar and bat mitzvah|B'nai Mitzvot]] and weddings are in $18 increments.<ref>{{Cite web|title=Chai, Its Meaning and Significance {{!}} Shiva, Jewish Mourning|url=https://www.shiva.com/learning-center/commemorate/chai|access-date=2020-11-18|website=www.shiva.com}}</ref>
 ==Age 18==
+{{see also|Age of majority|Voting age|Drinking age|Smoking age|Marriageable age|Age of consent}}
-I wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!! wish I was 18!!!!!
+In most countries, 18 is the [[age of majority]], in which a minor becomes a legal adult. It is also the [[voting age]], [[marriageable age]], [[drinking age]] and [[smoking age]] in most countries, though sometimes these ages are different than the age of majority.  Many [[Website|websites]] restrict adult content to visitors [[Minor (law)|who claim to be at least 18 years old.]]
+*In the United States, 18 is the:
+**[[age of consent|Age for sexual consent]] in eleven states and under federal law.<ref>{{cite web |url=https://aspe.hhs.gov/report/statutory-rape-guide-state-laws-and-reporting-requirements-summary-current-state-laws/sexual-intercourse-minors |title=STATUTORY RAPE: A GUIDE TO STATE LAWS AND REPORTING REQUIREMENTS. SEXUAL INTERCOURSE WITH MINORS |newspaper=Aspe|date=23 November 2015 }}</ref>
+**Minimum age to purchase firearms in thirty-eight states with the exception of handguns (21 under federal law).<ref>{{cite web |title=Minimum Age |url=https://giffords.org/lawcenter/gun-laws/policy-areas/who-can-have-a-gun/minimum-age/ |website=Giffords}}</ref>
+**[[Marriageable age]] without parental consent except for [[Nebraska]] (19), Mississippi and Puerto Rico (21).
+**The minimum age at which one can purchase, rent, or buy tickets to [[NC-17]]-rated films or buy video games with an [[Entertainment Software Rating Board|Adults Only]] rating.
+*In the UK, 18 is the legal age to purchase a [[British Board of Film Classification|BBFC]] "18" rated film.
+*In Japan, 18 is the minimum age at which one can purchase, rent, or buy tickets to [[Eirin|R18+]] rated movies or buy video games with a [[Computer Entertainment Rating Organization|Z]] rating, although 20 is their cultural age of adulthood.
 ==In sports==
+* In [[association football]] (soccer), "the 18" is a slang term for the [[penalty area]].
-* In [[Australian rules football]]:
+* In [[Nippon Professional Baseball]] (Japanese baseball), No.18 is known as the [[Ace (baseball)|Ace]] number.
-** Each team has 18 players on the field during play.
-** The [[Australian Football League]], the sport's top professional league, has had 18 teams since the [[2012 AFL season|2012 season]].
-* In [[association football]], "the 18" is a slang term for the [[penalty area]].
-* The [[Squad number|jersey number]] 18 has been [[Retired number|retired]] by several [[Major professional sports leagues in the United States and Canada|North American sports]] teams in honor of past playing greats or other key figures:
-** In [[Major League Baseball]]:
-*** The [[Cincinnati Reds]], for [[Ted Kluszewski]].
-*** The [[Cleveland Indians]], for [[Mel Harder]].
-** In the [[National Basketball Association|NBA]]:
-*** The [[Boston Celtics]], for [[List of players in the Naismith Memorial Basketball Hall of Fame|Hall of Famer]] [[Dave Cowens]]. The team initially planned to retire the number for [[Jim Loscutoff]], but he requested that the number not be retired at that time.
-** In the [[National Hockey League|NHL]]:
-*** The [[Buffalo Sabres]], for [[Danny Gare]].
-*** The [[Chicago Blackhawks]], for [[Hockey Hall of Fame|Hall of Famer]] [[Denis Savard]].
-*** The [[Montreal Canadiens]], for Hall of Famer [[Serge Savard]].
-*** The [[Los Angeles Kings]], for [[Dave Taylor (ice hockey)|Dave Taylor]].
-** In the [[National Football League|NFL]]:
-*** The [[Denver Broncos]], for [[Frank Tripucka]]. The number was taken out of retirement, with Tripucka's blessing, for [[Peyton Manning]], who wore the number with the [[Indianapolis Colts]].
-*** The [[Kansas City Chiefs]], for [[Pro Football Hall of Fame|Hall of Famer]] [[Emmitt Thomas]].
-*** The Colts have yet to retire any numbers during their history in Indianapolis, but have taken #18 out of circulation following Manning's departure from the team.
-** In addition, the [[Ole Miss Rebels football|University of Mississippi football program]] has retired #18 for [[Archie Manning]].
-* 18 is also the number of a [[NASCAR]] [[Sprint Cup Series]] car currently owned by [[Joe Gibbs Racing]]. The #18 has been driven by [[Kyle Busch]] since [[2008 NASCAR Sprint Cup Series|2008]]. Other notable drivers of the car include [[Dale Jarrett]], who won the [[1993 Daytona 500]] in the #18; [[Bobby Labonte]], who won the Cup championship in [[2000 NASCAR Winston Cup Series|2000]]; and [[J. J. Yeley]].
-* The number of holes on a regulation [[golf]] course
-==In other fields==
+==Notes==
+{{Notelist}}
-'''Eighteen''' is also:
-* 18:00, a time on the [[24-hour clock]] corresponding to [[12-hour clock|6:00 PM]].
-* A 2005 movie directed by [[Richard Bell (director)|Richard Bell]] and starring [[Brendan Fletcher]] and [[Alan Cumming]].
-* [[18 (Moby album)|A 2002 album]] by electronic artist [[Moby]].
-* The number of chapters into which [[James Joyce]]'s epic novel [[Ulysses (novel)|Ulysses]] is divided
-* Russ Wheeler's car number in the film ''[[Days of Thunder]]''
-*The number of wheels on the most common type of North American [[tractor-trailer]] truck, which are hence often called ''18-wheelers''
-*The number of the French department [[Cher (department)|Cher]] and the [[Provinces of Turkey|Turkish province]] [[Bitlis]]
-*[[DVD]]-18 is double-sided, double-layered DVD format
-*A Canon error message, see [[E18 error]]
-*In [[neo-Nazi]] circles, a [[code word]] for [[Adolf Hitler]]. The number comes from the position of the letters in the alphabet: [[A]] = [[1 (number)|1]], [[H]] = [[8 (number)|8]]. See also [[88 (number)#As a Neo-Nazi symbol|88]].
-*[[Cyborg 18|Android 18]], a fictional character in the ''Dragon Ball'' manga series.
-* [[18th Street gang]], a Hispanic American gang
-*The Hindu epic [[Mahabharata]] has eighteen sections, involves eighteen armies and is about a war fought over eighteen days
-* In some countries the number 18 means blood (relative)
-* In the Chinese mythos, [[Hell]] has 18 levels
-*In Chinese folklore, the [[Shaolin temple]] had a group of 18 bronze Monks. Initiates could only be considered full graduates of Shaolin [[martial art]]s if they could defeat them in combat.
-* In 1990 [[Megadeth]] released Hanger 18 as a single for the Rust in Piece Album.
-*[[Eighteen Visions]] (often abbreviated to 18V), an [[alternative metal]]/[[metalcore]] band from [[Orange County, California]].
-* Eighteen Eighteen, a [[South Africa]]n [[Rap artist]].
-* "[[I'm Eighteen]]", [[Alice Cooper]]'s first Top Ten hit single, from their 1971 album ''[[Love It to Death]]''.
-*Eighteen is also a surname, recorded in East Anglia in the 18th century <ref>{{cite web|url=http://www.one-name.org/profiles/eighteen.html#origin |title=Eighteen One-Name Study |publisher=One-name.org |date=2012-01-13 |accessdate=2013-08-02}}</ref>
-==See also==
+==References==
-*[[Numeral system]]
-==Notes==
 {{Reflist}}
 {{Integers|zero}}
+[[Category:Integers]]
-{{DEFAULTSORT:18 (Number)}}
-[[Category:Integers|1 8]]