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A '''number''' is an abstract [[mathematics|mathematical]] object hard to define. In mathematics, a number is formally a member of a given [[set]] (possibly an ordered set). It conveys the ideas of counting, ordering, and measurement. However, due to the expressiveness of [[positional number system]]s, the usefulness of [[geometry|geometric objects]], and the advances in different scientific fields, it can convey more properties and can be expressed in different notations. | A '''number''' is an abstract [[mathematics|mathematical]] object hard to define. In mathematics, a number is formally a member of a given [[set]] (possibly an ordered set). It conveys the ideas of counting, ordering, and measurement. However, due to the expressiveness of [[positional number system]]s, the usefulness of [[geometry|geometric objects]], and the advances in different scientific fields, it can convey more properties and can be expressed in different notations. | ||
Numbers are used to count (e.g., there are 26 simple [[latin alphabet|latin letter]]s). Numbers can be compared (e.g., [[e (math)|e]] is lower than [[pi]] in the [[real number]] set). In many [[natural | Numbers are used to count (e.g., there are 26 simple [[latin alphabet|latin letter]]s). Numbers can be compared (e.g., [[e (math)|e]] is lower than [[pi]] in the [[real number]] set). In many [[natural science]]s, they are used to measure (e.g., the weight of 50 lbs in [[imperial system]] is approximately equal to the mass of 22.7 kg in the [[metric system]]). | ||
A word written only with digits is called a [[numeral system|numeral]], and may represent a number. Numerals are often used for labeling (like [[telephone number]]s), for ordering (like [[serial number]]s), and for encoding (like [[ISBN]]s). | A word written only with digits is called a [[numeral system|numeral]], and may represent a number. Numerals are often used for labeling (like [[telephone number]]s), for ordering (like [[serial number]]s), and for encoding (like [[ISBN]]s). | ||
The writing of a number depends on the numeral system in use. For instance, the number 12 is written "1100" in [[binary numeral system|base 2]], "C" in [[hexadecimal numeral system|base 16]], and "XII" as a [[roman numeral]]. We can geometrically represent a number with [[vector]]s in a cartesian system or by drawing simple shapes (e.g., squares and circles). There are other means to express a number. | |||
Revision as of 04:34, 5 March 2008
A number is an abstract mathematical object hard to define. In mathematics, a number is formally a member of a given set (possibly an ordered set). It conveys the ideas of counting, ordering, and measurement. However, due to the expressiveness of positional number systems, the usefulness of geometric objects, and the advances in different scientific fields, it can convey more properties and can be expressed in different notations.
Numbers are used to count (e.g., there are 26 simple latin letters). Numbers can be compared (e.g., e is lower than pi in the real number set). In many natural sciences, they are used to measure (e.g., the weight of 50 lbs in imperial system is approximately equal to the mass of 22.7 kg in the metric system).
A word written only with digits is called a numeral, and may represent a number. Numerals are often used for labeling (like telephone numbers), for ordering (like serial numbers), and for encoding (like ISBNs).
The writing of a number depends on the numeral system in use. For instance, the number 12 is written "1100" in base 2, "C" in base 16, and "XII" as a roman numeral. We can geometrically represent a number with vectors in a cartesian system or by drawing simple shapes (e.g., squares and circles). There are other means to express a number.