Category:Real Numbers
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This category contains results about Real Numbers.
Definitions specific to this category can be found in Definitions/Real Numbers.
A real number is defined as a number which is identified with a point on the real number line.
Real Number Line
From the Cantor-Dedekind Hypothesis, the set of real numbers is isomorphic to any infinite straight line.
The real number line is an arbitrary infinite straight line each of whose points is identified with a real number such that the distance between any two real numbers is consistent with the length of the line between those two points.
Subcategories
This category has the following 48 subcategories, out of 48 total.
B
C
E
- Equality of Real Numbers (2 P)
- Examples of Real Numbers (1 P)
I
N
- Negative Real Numbers (empty)
P
- Positive Real Numbers (empty)
R
- Real Division (13 P)
- Real Number Line (empty)
S
- Strictly Negative Real Numbers (empty)
T
- Transitive Law (2 P)
U
- Unbounded Above Sets of Real Numbers (empty)
- Unbounded Below Sets of Real Numbers (empty)
- Unbounded Sets of Real Numbers (empty)
Pages in category "Real Numbers"
The following 92 pages are in this category, out of 92 total.
A
- User:Abcxyz/Sandbox/Real Numbers
- User:Abcxyz/Sandbox/Real Numbers/Identity for Real Addition
- User:Abcxyz/Sandbox/Real Numbers/Identity for Real Multiplication
- User:Abcxyz/Sandbox/Real Numbers/Inverses for Real Addition
- User:Abcxyz/Sandbox/Real Numbers/Inverses for Real Multiplication
- User:Abcxyz/Sandbox/Real Numbers/Ordering on Real Numbers is Compatible with Addition
- User:Abcxyz/Sandbox/Real Numbers/Ordering on Real Numbers is Total Ordering
- User:Abcxyz/Sandbox/Real Numbers/Real Addition is Associative
- User:Abcxyz/Sandbox/Real Numbers/Real Addition is Closed
- User:Abcxyz/Sandbox/Real Numbers/Real Addition is Commutative
- User:Abcxyz/Sandbox/Real Numbers/Real Multiplication Distributes over Addition
- User:Abcxyz/Sandbox/Real Numbers/Real Multiplication is Associative
- User:Abcxyz/Sandbox/Real Numbers/Real Multiplication is Closed
- User:Abcxyz/Sandbox/Real Numbers/Real Multiplication is Commutative
- User:Abcxyz/Sandbox/Real Numbers/Real Numbers are Dedekind Complete
- Algebraic Closure of Real Number Field is Complex Number Field
C
- Canonical Injection of Real Number Line into Complex Plane
- Characterizing Property of Infimum of Subset of Real Numbers
- Characterizing Property of Supremum of Subset of Real Numbers
- Choice Function/Examples/Doubletons of Real Numbers
- Condition for Element of Quotient Group of Additive Group of Reals by Integers to be of Finite Order
- Continuum Property implies Well-Ordering Principle
- Convergent Real Sequence has Unique Limit
- Cross-Relation on Real Numbers is Equivalence Relation
E
F
I
O
P
Q
R
- Rational Numbers form Subfield of Real Numbers
- Rational Numbers form Subset of Real Numbers
- Real Number between Zero and One is Greater than Power/Natural Number
- Real Number Inequalities can be Added
- Real Number is Greater than Zero iff its Negative is Less than Zero
- Real Number is not necessarily Rational Number
- Real Number Line is Metric Space
- Real Number Line is not Topological Continuum
- Real Numbers are Densely Ordered
- Real Numbers are not Well-Ordered under Conventional Ordering
- Real Numbers are Uncountably Infinite
- Real Numbers form Algebra
- Real Numbers form Field
- Real Numbers form Integral Domain
- Real Numbers form only Ordered Field which is Complete
- Real Numbers form Ordered Integral Domain
- Real Numbers form Perfect Set
- Real Numbers form Ring
- Real Numbers form Subfield of Complex Numbers
- Real Numbers form Totally Ordered Field
- Real Numbers form Valued Field
- Real Numbers form Vector Space
- Real Vector Space is Vector Space
- Real Zero is Less than Real One
- Real Zero is Zero Element
- Reals are Isomorphic to Dedekind Cuts
- Reciprocal of Real Number is Non-Zero
- Reciprocal of Strictly Negative Real Number is Strictly Negative
- Reciprocal of Strictly Positive Real Number is Strictly Positive
S
- Set of Non-Negative Real Numbers is not Well-Ordered by Usual Ordering
- Set of Subsets of Reals with Cardinality less than Continuum Cardinality of Local Minimums of Union Closure less than Continuum
- Square of Non-Zero Real Number is Strictly Positive
- Square Root is Strictly Increasing
- Sub-Basis for Real Number Line
- Subgroup of Real Numbers is Discrete or Dense
- Sum of Indices of Real Number