Changes

*Any decimal representation which terminates (comes to an end), like 6.023, because this is just a way of writing a fraction (in this case, 6023/1000)

*Any decimal representation which terminates (comes to an end), like 6.023, because this is just a way of writing a fraction (in this case, 6023/1000)

*Any decimal representation which repeats or recurs, like 1.86292929292929..., because these can be shown to be fractions{{prove}}

*Any decimal representation which repeats or recurs, like 1.86292929292929..., because these can be shown to be fractions{{prove}}

*[[Irrational numbers]], like &sqrt;10 = 3.162277660168... π = 3.1415926525..., whose decimal representations never repeat or terminate.{{prove}}

*[[Irrational numbers]], like <math>\sqrt{10} = 3.162277660168...</math>&pi; = 3.1415926525..., whose decimal representations never repeat or terminate.

==Formal definition==

==Formal definition==

Formally, real numbers are defined as the unique [[Field (mathematics)|field]] which is [[Ordered]], [[Complete (mathematics)|Complete]], and [[Archimedean]]. The reals can be constructed from the rationals by means of [[Dedekind cuts]] or [[Cauchy Sequences]], i.e. it is the compeletion of the [[metric space]] of rational numbers.

Formally, real numbers are defined as the unique [[Field (mathematics)|field]] which is [[ordered]], [[Complete (mathematics)|complete]], and [[Archimedean]]. The reals can be constructed from the rationals by means of [[Dedekind cuts]] or [[Cauchy Sequences]], i.e. it is the completion of the [[metric space]] of rational numbers.

==Infinity==

==Infinity==