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"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
In alphabetic numeral systems, numbers are written using the characters of an alphabet, syllabary, or another writing system. Unlike acrophonic numeral systems , where a numeral is represented by the first letter of the lexical name of the numeral, alphabetic numeral systems can arbitrarily assign letters to numerical values.
The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number eleven in the decimal or base-10 numeral system (today, the most common system globally), the number three in the binary or base-2 numeral system (used in modern computers), and the number two in the unary numeral ...
In mathematics, a lexicographical order is the generalization of the alphabetical order to other data types, such as sequences of numbers or other ordered mathematical objects. When applied to strings or sequences that may contain digits, numbers or more elaborate types of elements, in addition to alphabetical characters, the alphabetical order ...
Numbers in mathematical formulae are never spelled out (3 < π < 22 / 7 not three < pi < twenty-two sevenths), and "numbers as numbers" are rarely spelled out in other mathematical contexts (the first three primes are 2, 3, and 5 not the first three primes are two, three, and five; but zero-sum game and roots of unity).
So too are the thousands, with the number of thousands followed by the word "thousand". The number one thousand may be written 1 000 or 1000 or 1,000; larger numbers are written for example 10 000 or 10,000 for ease of reading. European languages that use the comma as a decimal separator may correspondingly use the period as a thousands separator.
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The schemes can be considered to be examples of a primary key of a database management system table, whose table definitions require a database design. In computability theory , the simplest numbering scheme is the assignment of natural numbers to a set of objects such as functions , rational numbers , graphs , or words in some formal language .