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== Extension of logarithms to non-natural number exponents ==

...egrees. He considered all kinds of [[real number]]s on an equal footing—[[natural number]]s, roots (the majority of which are [[irrational number]]s), and negativ

...are [[uncountable]]; that is, there are strictly more real numbers than [[natural number]]s, even though both sets are [[infinite set|infinite]]. In fact, the [[car

where <math>N</math> is natural number; usually, <math>N=2^q</math> for some natural <math>q</math>;<br>

...t style = "vertical-align: 17%"><math>\mathbb{R}^n</math></font> for any [[natural number]] ''n''; or the [[complex number|complex plane]] or powers of it, <font st

: ''n'' is a [[natural number]] that plays the role of [[principal quantum number]], ''n'' = 1,2,...,

:''A'' = {x | 1 < x < 10, x is a natural number} ...as follows: A is the set of all x, where x is between 1 and 10, and x is a natural number. A could also be written as:

for some [[natural number|natural]] <math>n</math> such that <math>|f^{-n}(z)|\ll 1</math>.

...of a [[numerator]] (an [[integer]] — the part) and a [[denominator]] (a [[natural number]] — the whole). For instance, the fraction <math> \scriptstyle \frac{3}{5 ...Equivalent fractions|equivalent fraction]] with an integer numerator and a natural number denominator. A fraction with equal numerator and denominator is equal to on

...venient proof that the set <math>2^{\mathbb{N}}</math> of subsets of the [[natural number]]s (also known as its [[power set]]) is not [[countable set|countable]]. Mo

...e cases, when number <math>n</math> of iterations can be simplified to a [[natural number]], expressed with integer constant. Attempts to call [[Nest]] to evaluate a

...and the magnetic quantum number ''m''. These three quantum numbers are [[natural number]]s, their definitions and ranges are:

is used for the ''q''-analogue of a natural number ''n''.

...ven if some of these operations are not yet defined, <math>z^n</math> for natural number <math>n</math> can be considered as just iteration of function "multiplica

...ves, and zero, this is incorrect. ''Whole number'' should be replaced by ''natural number'' or by ''positive whole number.'' ...and especially the first sentence, accessible for everybody. "Integer" or "natural number" might be a problem. However, we also want to be correct. I think that "pos

...]] elements that have the property that ''a''^''n'' = 0 for some natural number ''n''. Most of these properties are now very well-known for matrices, whic

...st also be greater than zero, so <math>n</math> is restricted to being a [[natural number]], <math>1,2,3,...</math>.

== Natural number/Related Articles == Daniel, you and Howard have edited [[Natural number/Related Articles]].

The study of quantity starts with [[number]]s, first the familiar [[natural number]]s and [[whole number]]s and arithmetical operations on them, which are cha | [[Natural number]]s|| [[Whole number]]s|| [[Integer]]s || [[Rational number]]s || [[Real num

...''typed'' functions. For example if we consider the function that takes a natural number and doubles it, we may regard this as a function from '''N''' to '''N''', b