Properties
Tallying is often referred to as "base 1", since only one mark – the tally itself – is needed. This is more formally referred to as a unary numeral system. Unlike base 2 or base 10, this is not a positional notation. Since the base 1 exponential function (1x) always equals 1, its inverse does not exist (which would be called the logarithm base 1 if it did exist). There are two ways to write the real number 1 as a recurring decimal: as 1.000..., and as 0.999.... 1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few. In many mathematical and engineering problems, numeric values are typically normalized to fall within the unit interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters. Likewise, vectors are often normalized into unit vectors (i.e., vectors of magnitude one), because these often have more desirable properties. Functions, too, are often normalized by the condition that they have integral one, maximum value one, or square integral one, depending on the application. Because of the multiplicative identity, if f(x) is a multiplicative function, then f(1) must be equal to 1. It is also the first and second number in the Fibonacci sequence (0 being the zeroth) and is the first number in many other mathematical sequences. The definition of a field requires that 1 must not be equal to 0. Thus, there are no fields of characteristic 1.
Primality
1 is by convention neither a prime number nor a composite number, but a unit (meaning of ring theory) like −1 and, in the Gaussian integers, i and −i. The fundamental theorem of arithmetic guarantees unique factorization over the integers only up to units. For example, 4 = 22, but if units are included, is also equal to, say, (−1)6 × 123 × 22, among infinitely many similar "factorizations". 1 appears to meet the naïve definition of a prime number, being evenly divisible only by 1 and itself (also 1). As such, some mathematicians considered it a prime number as late as the middle of the 20th century, but mathematical consensus has generally and since then universally been to exclude it for a variety of reasons (such as complicating the fundamental theorem of arithmetic and other theorems related to prime numbers). 1 is the only positive integer divisible by exactly one positive integer, whereas prime numbers are divisible by exactly two positive integers, composite numbers are divisible by more than two positive integers, and zero is divisible by all positive integers. Table of basic calculations
In technology
The resin identification code used in recycling to identify polyethylene terephthalate. The ITU country code for the North American Numbering Plan area, which includes the United States, Canada, and parts of the Caribbean. A binary code is a sequence of 1 and 0 that is used in computers for representing any kind of data. In many physical devices, 1 represents the value for "on", which means that electricity is flowing.