| Number: | 2 |
| Ordinal: | 2nd (second / twoth) |
| Numeral: | binary |
| Gaussian Integer Factorization: | (1+i)(1-i) |
| Prime: | 1st |
| Divisor: | 1, 2 |
| Roman: | II, ii |
| Greek Prefix: | di- |
| Latin Prefix: | duo-/bi- |
| Old English Prefix: | twi- |
| Lang1: | Greek numeral |
| Lang1 Symbol: | β' |
| Lang2: | Arabic, Kurdish, Persian, Sindhi, Urdu |
| Lang3: | Ge'ez |
| Lang3 Symbol: | ፪ |
| Lang4: | Bengali |
| Lang5: | Chinese numeral |
| Lang5 Symbol: | 二，弍，貳 |
| Lang6: | Devanāgarī |
| Lang7: | Telugu |
| Lang8: | Tamil |
| Lang9: | Kannada |
| Lang10: | Hebrew |
| Lang11: | Armenian |
| Lang11 Symbol: | Բ |
| Lang12: | Khmer |
| Lang12 Symbol: | ២ |
| Lang13: | Maya numerals |
| Lang13 Symbol: | •• |
| Lang14: | Thai |
| Lang14 Symbol: | ๒ |
| Lang15 Symbol: | (Bani) |
| Lang16: | Malayalam |
| Lang16 Symbol: | ൨ |
| Lang17: | Babylonian numeral |
| Lang18: | Egyptian hieroglyph, Aegean numeral, Chinese counting rod |
| Lang19: | Morse code |
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and the only even prime number.
Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.
Two is most commonly a determiner used with plural countable nouns, as in two days or I'll take these two.[1] Two is a noun when it refers to the number two as in two plus two is four.
The word two is derived from the Old English words English, Old (ca.450-1100);: twā (feminine), English, Old (ca.450-1100);: tū (neuter), and English, Old (ca.450-1100);: twēġen (masculine, which survives today in the form twain).
The pronunciation pronounced as //tuː//, like that of who is due to the labialization of the vowel by the w, which then disappeared before the related sound. The successive stages of pronunciation for the Old English English, Old (ca.450-1100);: twā would thus be pronounced as //twɑː//, pronounced as //twɔː//, pronounced as //twoː//, pronounced as //twuː//, and finally pronounced as //tuː//.
An integer is determined to be even if it is divisible by two. For integers written in a numeral system based on an even number such as decimal, divisibility by two is easily tested by merely looking at the last digit. If it is even, then the whole number is even. When written in the decimal system, all multiple of 2 will end in 0, 2, 4, 6, or 8.[2]
1 is neither prime nor composite yet odd. 0, which is an origin to the integers in the real line, especially when considered alongside negative integers, is neither prime nor composite, however it is distinctively even (as a multiple of two) since if it were to be odd, then for some integer
k
0=2k+1
k
-\tfrac{1}{2}
f(x)=0
2 is the smallest and the only even prime number. As the smallest prime number, two is also the smallest non-zero pronic number, and the only pronic prime.[3]
d(n)
n
\liminf
d(n)
2
(0,1)\inN0
1
0
0
\tfrac{0}{0}
(0,2)\inN0
Meanwhile, the numbers two and three are the only two prime numbers that are consecutive integers. Two is the smallest isolated prime, i.e., the first prime number that is not a twin prime.[5] [6] Because two has more divisors than any smaller positive integer, it is a highly composite number,[7] being the only number that is both prime and highly composite.
Twin primes are the smallest type of prime k-tuples, that represent patterns of repeating differences between prime numbers. A difference of two in prime k-tuples exists inside prime quintuplets, and in some types of prime triplets and prime quadruplets (etc.).
2
\pi(x)-\pi\left(
| x | |
| 2 |
\right)\ge1,2,3,\ldotsforallx\ge2,11,17,\ldots
\pi(x)
x
A set that is a field has a minimum of two elements. In a set-theoretical construction of the natural numbers
N
\{\varnothing,\{\varnothing\}\}
\varnothing
\{0,1\}=\{\varnothing,\{\varnothing\}\}
2S
2\kappa>\kappa
2N
\{0,1\}
[0,1]
xn+1=rxn(1-xn)
r=4.
r ≈ 3.45
3.57
8,16,...,2n,\ldots,2infty
Powers of two are essential in computer science, and important in the constructability of regular polygons using basic tools (e.g., through the use of Fermat or Pierpont primes).
2
| infin | |
| \sum | |
| n=0 |
| 1 | =1+ | |
| 2n |
| 1 | + | |
| 2 |
| 1 | + | |
| 4 |
| 1 | + | |
| 8 |
| 1 | |
| 16 |
+ … =2.
Two also has the unique property that
2+2=2 x 2=22=2\uparrow\uparrow2=2\uparrow\uparrow\uparrow2=...
4.
Notably, row sums in Pascal's triangle are in equivalence with successive powers of two,
2n.
A number is perfect if it is equal to its aliquot sum, or the sum of all of its positive divisors excluding the number itself. This is equivalent to describing a perfect number
n
\sigma(n)
2n.
6
1
2
n
n
n
1.
Also,
\limsupn\toinfty
| logd(n) | |
| logn/loglogn |
=log2