Beyond this, natural numbers are widely used as a building block for other number systems including the integers, rational numbers and real numbers. The natural numbers are a subset of the integers and are of historical and pedagogical value as they can be used for counting and often have ethno-cultural significance (see below). The distinction is drawn between the number five (an abstract object equal to 2+3), and the numeral five (the noun referring to the number). This list focuses on numbers as mathematical objects and is not a list of numerals, which are linguistic devices: nouns, adjectives, or adverbs that designate numbers. This list will also be categorised with the standard convention of types of numbers. For example, the pair of numbers (3,4) is commonly regarded as a number when it is in the form of a complex number (3+4i), but not when it is in the form of a vector (3,4). The definition of what is classed as a number is rather diffuse and based on historical distinctions.
This is known as the interesting number paradox. Even the smallest "uninteresting" number is paradoxically interesting for that very property. Numbers may be included in the list based on their mathematical, historical or cultural notability, but all numbers have qualities which could arguably make them notable. The list does not contain all numbers in existence as most of the number sets are infinite. This is a list of notable numbers and articles about notable numbers. You can help by adding missing items with reliable sources. This is a dynamic list and may never be able to satisfy particular standards for completeness.
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