219 (two hundred
ndnineteen) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
following
218
Year 218 ( CCXVIII) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Severus and Adventus (or, less frequently, year 971 ''Ab urbe c ...
and preceding
220
__NOTOC__
Year 220 ( CCXX) was a leap year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Antonius and Eutychianus (or, less frequently, year 973 '' ...
.
In mathematics
*219 is a
happy number
In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because ...
.
*
Mertens function
In number theory, the Mertens function is defined for all positive integers ''n'' as
: M(n) = \sum_^n \mu(k),
where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive re ...
(219) = 4, a record high.
*There are 219
partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a bina ...
s on four labeled elements.
*219 is the smallest number that can be represented as a sum of four positive cubes in two different ways.
[.]
*There are 219 different
space group
In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it uncha ...
s, discrete and full-dimensional sets of symmetries of three-dimensional space or of crystal structures.
References
Integers
{{Num-stub