- high-resolution terminology - matching measurements at high-resolution
Number
Description
[[Description::A number N is a count NX [x] of elementary entity X divided by the unit-entity UX [x]. X must represent the same entity in both occurences. The counting-unit [x] cancels by division, such that numbers (for example, numbers 8 or 24) are abstracted from the counted entity (we write 8 and 24, although 8 x·x-1 and 24 x·x-1 would be equally correct; distinguished from a count of 8 x or 24 x if we count an entity-type X=apple). It is difficult to separate the concept of 'number' from the realization of number words or number symbols. Consider the symbol 9 written into MitoPedia as elementary entity X=9. Then counting "9 9 9 9 9 9 9 9" yields a count N9 = 8 x, and the count N9 [x] divided by the unit-entity U9 [x] yields the number N = 8. The human number concept has not only quantitative cardinal meaning related to the count (8 or 24 elementary entities), but is applied in expressing the ordinal rank of objects or events arranged in a sequence (in the Fibonacci-sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, .. the 8th number is 13, whereas in an older representation of the Fibonacci-sequence 1, 1, 2, 3, 5, 8, 13, 21, .. the 5th number is 5; the 24th day of a month), and in nominal labelling (drawing lot #24). Counting numbers (1, 2, 3, 4, 5, 6, 7, 8, ..) are unified multiplicities required for cardinal counting or ordinal nomination of the endpoint in a sequence. It is debateable, if one can have a zero count; a no-object, or an object that is not there to be counted. If this possibility is not denied, then counting numbers are equivalent to natural or whole numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, ..). Numbers are represented by words, iconic symbols, or entirely abstract symbols. The word 'snake', the word 'eight', the symbol '8' written in ink on a piece of white paper are as different from the real "object snake", as they differ from the "concept ////////", or "concept §§§§§§§§", or "concept 88888888", or "concept ∞∞∞∞∞∞∞∞", or "concept 'number eight'". We are so deeply used to these symbols, that we easily take the iconic or abstract symbol 8 — that represents the number eight — as the number eight itself, without a need to give the symbol 8 an interpretation and ask for its meaning.]]
Abbreviation: Has abbr::''N''
Communicated by Gnaiger Erich 2020-06-27
A taxonomy of numbers
Name Example Comment counting number, natural number 1, 2, 3, 4, .. Positive integers. All natural numbers are whole numbers. whole number 0, 1, 2, 3, 4, .. Positive integers including zero. All whole numbers are integers. integer .., -4, -3, -2, -1, 0, 1, 2, 3, 4, .. Negative integers, zero, and positive integers. All integers are rational numbers. rational number -2/1, -0.5, 0.0, 0.3, 1/2, 7.8 Any number that can be written as a ratio of two integers — where the denominator must not be zero —, or as the resulting fraction written with decimal places. All rational numbers are real numbers, and are not imaginary numbers. irrational number square root of 2; √2 Irrational numbers cannot be written as a ratio of two integers; the have an infinite number of decimal places. real number Real numbers include all types of numbers listed above and are defined as points on a line from -∞ to +∞. immaginary number square root of -1 An imaginary number squared yields a negative real number. complex number Complex numbers are combinations of real and imaginary numbers.
References
{{#ask:Additional label::Number | mainlabel=Bioblast link |?Has title=Reference |?Was published in year=Year |format=broadtable |limit=5000 |offset=0 |sort=Has title |order=ascending }}
MitoPedia concepts:
Ergodynamics
