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((Navbox
| name = Number systems
| state = (({state<includeonly>|autocollapse</includeonly>))}
| title = [[Number]] systems
| listclass = hlist

| group1 = Sets of [[definable number]]s
| list1 =
* [[Natural number]]s&nbsp;(<math>\mathbb N</math>)
* [[Integer]]s&nbsp;(<math>\mathbb Z</math>)
* [[Rational number]]s&nbsp;(<math>\mathbb Q</math>)
* [[Constructible number]]s
* [[Algebraic number]]s&nbsp;(<math>\mathbb A</math>)
* [[Closed-form_expression#Closed-form_number|Closed-form number]]s
* [[Period (algebraic geometry)|Periods]]
* [[Computable number]]s
* [[Definable real number#Definability in arithmetic|Arithmetical numbers]]
* [[Definable real number#Definability in models of ZFC|Set-theoretically definable numbers]]
* [[Gaussian integer]]s

| group2 = [[Composition algebra]]s
| list2=
* [[Division algebra]]s: [[Real number]]s&nbsp;(<math>\Reals</math>)
* [[Complex number]]s&nbsp;(<math>\Complex</math>)
* [[Quaternion]]s&nbsp;(<math>\mathbb H</math>)
* [[Octonion]]s&nbsp;(<math>\mathbb O</math>)

| group3 = Split<br>types
| list3 = 
* Over <math>\Reals</math>:
* [[Split-complex number]]s
* [[Split-quaternion]]s
* [[Split-octonion]]s<br> Over <math>\Complex</math>:
* [[Bicomplex number]]s
* [[Biquaternion]]s
* [[Bioctonion]]s

| group4 = Other [[hypercomplex number|hypercomplex]]
| list4 =
* [[Dual number]]s
* [[Dual quaternion]]s
* [[Dual-complex number]]s
* [[Hyperbolic quaternion]]s
* [[Sedenion]]s &nbsp;(<math>\mathbb S</math>)
* [[Split-biquaternion]]s
* [[Multicomplex number]]s
* [[Geometric algebra]]/[[Clifford algebra]] 
** [[Algebra of physical space]]
** [[Spacetime algebra]]
** [[Plane-based geometric algebra]]

| group5 = Other types
| list5 =
* [[Cardinal number]]s
* [[Extended natural numbers]]
* [[Irrational number]]s
* [[Fuzzy number]]s
* [[Hyperreal number]]s
* [[Levi-Civita field]]
* [[Surreal number]]s
* [[Transcendental number]]s
* [[Ordinal number]]s
* [[P-adic number|((nowrap|''p''-adic)) numbers]] ([[Solenoid (mathematics)#p-adic solenoids|((nowrap|''p''-adic)) solenoids]])
* [[Supernatural number]]s
* [[Profinite integer]]s
* [[Superreal number]]s
* [[Normal number]]s

| belowclass = hlist
| below =
* [[Number#Main classification|Classification]]
* ((icon|list)) [[List of types of numbers|List]]

))<noinclude>
((Documentation))
</noinclude>

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