section_path: Mathematics/Elementary algebra
section_name: Elementary algebra
paragraph_text: Elementary algebra
  
  The number 0 is the smallest nonnegative integer, and the largest nonpositive integer. The natural number following 0 is 1 and no natural number precedes 0. The number 0 may or may not be considered a natural number, but it is an integer, and hence a rational number and a real number. All rational numbers are algebraic numbers, including 0. When the real numbers are extended to form the complex numbers, 0 becomes the origin of the complex plane.
  
  The number 0 can be regarded as neither positive nor negative or, alternatively, both positive and negative and is usually displayed as the central number in a number line. Zero is even (that is, a multiple of 2), and is also an integer multiple of any other integer, rational, or real number. It is neither a prime number nor a composite number: it is not prime because prime numbers are greater than 1 by definition, and it is not composite because it cannot be expressed as the product of two smaller natural numbers. (However, the singleton set {0} is a prime ideal in the ring of the integers.)
  
  The following are some basic rules for dealing with the number 0. These rules apply for any real or complex number x, unless otherwise stated.
  
  The expression 0 / 0, which may be obtained in an attempt to determine the limit of an expression of the form f (x) / g (x) as a result of applying the lim operator independently to both operands of the fraction, is a so-called " indeterminate form ". That does not mean that the limit sought is necessarily undefined; rather, it means that the limit of f (x) / g (x), if it exists, must be found by another method, such as l'Hôpital's rule.
  
  The sum of 0 numbers (the empty sum) is 0, and the product of 0 numbers (the empty product) is 1. The factorial 0! evaluates to 1, as a special case of the empty product.