Two
| Two | |
|---|---|
| 2 | |
| presentation | |
| Roman | II |
| dual | 10 |
| Octal | 2 |
| Duodecimal | 2 |
| Hexadecimal | 2 |
| Morse code | · · - - - |
| Arabic | ٢ |
| Chinese | 二 ， 弍 ， 贰 ， 貳 |
| Indian | २ |
| Mathematical properties | |
| sign | positive |
| parity | straight |
| Factorization | |
| Divider | 1.2 |
The two (2) is the natural number between one and three . It's even and a prime number .
mathematics
- Two is the smallest and the only even prime number, and the only one immediately followed by another (the 3).
- All even numbers are divisible by 2.
- Two is the third number in the Fibonacci sequence .
- Gottfried Wilhelm Leibniz discovered the dual system ( binary system or twosystem ), which only uses two digits to represent numbers. It experienced widespread use with the development of digital technology . Because of this, it is the best known and most important number system next to the commonly used decimal system .
- Two is a Størmer number .
Spellings
The Arabic numeral
An original numeral for the number two was formed from two parallel lines, horizontally (like the Chinese character (二) and the Brahmi number ) or vertically. From the Brahmi number, through the mediation of the Arabs, today's numeral 2 developed (see illustration).
Other numerals
The Roman numeral is II.
Linguistic
The number two has its own word in all spoken languages. In some cases, however, so-called indigenous peoples such as the Torres Strait Islanders only know their own word stems for the 1 and the 2. With these two they combine the numbers 3, 4, 5 and 6. They designate all numbers that come after them only with "a lot". There are also cases in which a language does not have any numbers, as in Pirahã .
Two
The German numeral two arose from the Indo-European root * duwo or * duôu and goes back to the neuter form two , which is already used in Old High German (the female form was two , the male two ). Further formations from this Indo-European root are for example the words Zuber, Zweck, Zweifel, Zwilling, Zwirn, Zwist and Zwitter .
Cardinal number
Up until the 18th century , Standard German distinguished the three grammatical genders for the number two . In some dialects of Swiss German , Bavarian and Moselle Franconian , these distinctions are still common, whereby neuter can stand for mixed-sex couples.
Declination:
| case | without article and with noun (two children) |
with article and noun (the two children) |
without article and without noun (two) |
||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| male | Female | neutrally | male | Female | neutrally | male | Female | neutrally | |||
| Nominative | two | two | two | two | two | two | two | two | two | ||
| Genitive | zweener | two | two | two | two | two | zweener | two | two | ||
| dative | two | two | two | two | two | two | two | two | two | ||
| accusative | two | two | two | two | two | two | two | two | two | ||
- In older orthography there is also zwen for two and two for two .
In the Old Testament, for example, Luther translates :
- “And you shall make chains for the shield with two ends, but the links hanging together, made of fine gold, and two gold rings on the shield, so that you attach the same two rings to two corners of the shield and the two gold chains in the same Put two rings on the two corners of the shield. "( Exodus 28 : 22-24)
In later times there was uncertainty and inconsistency in the use of these forms, until the distinction between the sexes finally became completely out of date; the inflection of two is omitted today except for the genitive and even more rarely the dative entirely, if the form is unambiguous.
The also outdated form zwier for “twice” comes from the genitive two , as in Luther's case: I fast two a week. ( Luke 18:12)
With the advent of electronic voice connections (telephone and radio), the form two became commonplace for two in order to be able to better distinguish the word from the similarly sounding " three " in the case of poor transmission quality . In Germany this sound was transferred to general business dealings and colloquial language. The "Zwo" is now less widespread, but "Zwo" is still used in radiotelephony, which reduces the risk of confusion. This applies to the fire brigade and in everyday operations in the Federal Armed Forces , the Federal Armed Forces and the Swiss Army . In Skat gamblers it is for the stimulus value consistently 22nd In the Bavarian language area, the distinctive function in everyday life is fulfilled by the Bavarian variants zwoa / zwà .
The prefix zwie- is derived from the numeral two , which defines the duality, as in the case of rusk or dichotomy .
The Greek word for two (δύο - dyo ) and the Latin duo can be found in numerous loan words, examples: Dyadik, Hendiadyoin , Duo , Duell , Dual , Duett .
The prefixes (Latin) bi- : binational , bimetal , bisexuality , and (Greek) δι- (di-) : dichotomy , diode , diptych also come from said Indo-European root .
Atomic number
The German atomic number of the second match in Latin secundus (actually "following") and Greek δεύτερος (deuteros) , in words like seconds , Sekundogenitur , deuterium and deuteron have been received.
Multiplicative number
In addition to twofold and twofold , the word doppel (from the Latin duplus ) has developed in German . The Latin duplus or duplex is part of numerous loan words, cf. Duplex , duplicate , duplicate . Words such as diplodocus and diploidy come from the corresponding Greek διπλόος ( diploos - double) .
Both
From the Indo-European root * ambho , shortened * bho , which also denotes a duality or pair, the New High German numeral both , which is declined like an adjective and two a unit or one , arose from the Old High German expression in diu ("both these") Describes things that form a couple. Only in modern times did the singular form develop into both .
The Greek dual form ἄμφω ( ampho - both) and the preposition ἀμφί ( amphi - on both sides, both-) and the synonymous Latin ambo or ambi come from the same root . They appear in numerous loanwords. Examples of this are amphitheater ("theater surrounded by spectators on both sides"), amphibium (living being living in both elements (water and air)), ambivalence ("validity of both (opposing) sides"), amphora ("handle on both sides") ) and ambiguity ("ambiguity").
The dual
In many languages there was or is a separate number for the two number , the dual . Remnants in German are the Bavarian pronouns eß for “you” and enk for “you” (which are now general plural forms). Indo-European languages that still express the dual are, for example, Slovene , Macedonian and Sorbian .
Plural and singular equivalents
For some objects that consist of two identical halves, plural forms are always used in languages such as English, French etc., but in German they are considered a unit and singular forms are used.
Examples:
- English: Where are my eyeglasses? - They are in the living room.
- French: Où sont mes lunettes? - Elles sont dans le salon.
- But in German: where are my glasses? - She's in the living room.
In German you can create plural forms of such words and combine them with number words (“a pair of glasses, two glasses”), in other languages you have to use paraphrases (“a pair of eyeglasses, two pairs of eyeglasses”, “une paire de lunettes”) , deux paires de lunettes “).
An exception is the (one pair) pants , which are still in use at least regionally - because of the two legs - as an alternative to pants .
Natural sciences
A large part of the animal kingdom, including all vertebrates and with them humans, belong to the Bilateria , whose bodies are mirror-symmetrical. Many organs therefore exist twice or in pairs. Some of the human perception is shaped by this symmetry of the body, for example the terms left and right .
Almost all living beings of higher organizational levels reproduce as two sexes. The separation of mankind into two genders, i.e. man and woman , has a lasting impact on self-perception and self-confidence.
In nuclear physics , two is one of the magic numbers as two protons or neutrons fill a shell.
Humanities, religion, mythology and literature
Two elements that together form a unit can be called a pair . Two opposed elements, which face each other or exclude form an opposed pair in the sense of polarity . In order to be able to classify or differentiate something, at least one pair of opposites is required, i.e. at least two distinguishable properties are present. A certain symmetry can be seen in every pair.
Logic , for example, speaks of the principle of two- valued value when the truth value true or false can be assigned to a fact . The ethics deals with the pair of opposites good and evil . Many religions also see the world in the tension of good and bad and sometimes use metaphysical ideas to cover these terms, for example of God and the devil or heaven and hell .
The Chinese numerology and its religious expression of Daoism see in the polarity of Yin and Yang in the system of Taiji the opposition, which determines the entire cosmos.
Brothers and Sisters
A common mythological and literary motif is that of the two brothers who hate each other or are at odds, and one of whom even kills the other on occasion. Examples are Cain and Abel from the Old Testament or Romulus and Remus from Roman mythology . There are also often 'harmonious' pairs of brothers, the Dioscurs from Greek mythology have become the proverbial for a lifelong friendship. Many of these pairs of brothers are twins - the fascination for the similarity or confusion between two brothers served as inspiration for some literary works, for example the children's book Das doppelte Lottchen by Erich Kästner .
An example of two sisters from the fairy tale are Goldmarie and Pechmarie from the fairy tale Frau Holle , which was recorded by the Brothers Grimm . As in many fairy tales, however, this is a half-sister couple.
Mixed pairs of siblings are also a common motif in legend and literature. In Greek mythology, Apollo and Artemis stand for sun and moon, or day and night. Famous fairy tale characters are little brothers and sisters and Hansel and Gretel . A motif often associated with sibling pairs is that of incest : incestuous relationships between siblings can be found in many creation myths , in literature the range extends from the siblings Siegmund and Sieglinde in Richard Wagner's Die Walküre and Thomas Mann's Wälsungenblut to the soap opera Verbotene Liebe on German television .
Web links
References and comments
- ^ Friedrich Kluge , Alfred Götze : Etymological dictionary of the German language . 20th ed., Ed. by Walther Mitzka , De Gruyter, Berlin / New York 1967; Reprint (“21st unchanged edition”) ibid 1975, ISBN 3-11-005709-3 , p. 894.
- ^ The dictionary of origin (= Der Duden in twelve volumes . Volume 7 ). Reprint of the 2nd edition. Dudenverlag, Mannheim 1997 ( p. 838 ). See also DWDS ( "two" ) and Friedrich Kluge : Etymological dictionary of the German language . 7th edition. Trübner, Strasbourg 1910 ( p. 512 ).
- ^ Johann Christoph Gottsched : Foundation of the German language art . Section From Numerals. ( at zeno.org )
- ↑ See also Eugen Stulz: The declination of the numeral "two" from XV. to XVIII. Century. In Zeitschrift für deutsche Wortforschung 2, 1902, pp. 85–117.