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In mathematics, the affinely extended real number system is obtained from the real number system by adding two infinity elements: and where the infinities are treated as actual numbers. It is useful in describing the algebra on infinities and the various limiting behaviors in calculus and mathematical analysis, especially in the theory of measure and integration. The affinely extended real number system is denoted or or It is the Dedekind–MacNeille completion of the real numbers. When the meaning is clear from context, the symbol is often written simply as

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rdfs:label	Extended real number line (en)
rdfs:comment	In mathematics, the affinely extended real number system is obtained from the real number system by adding two infinity elements: and where the infinities are treated as actual numbers. It is useful in describing the algebra on infinities and the various limiting behaviors in calculus and mathematical analysis, especially in the theory of measure and integration. The affinely extended real number system is denoted or or It is the Dedekind–MacNeille completion of the real numbers. When the meaning is clear from context, the symbol is often written simply as (en)
sameAs	Extended real number line Extended real number line
dbp:wikiPageUsesTemplate	dbt:About dbt:Citation dbt:Efn dbt:Large_numbers dbt:Math dbt:MathWorld dbt:Notelist dbt:Real_numbers dbt:Section_link dbt:Short_description
Subject	Real numbers Infinity
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Extended_real_number_line?oldid=1068430390&ns=0
Wikipage page ID	51698 (xsd:integer)
page length (characters) of wiki page	13598 (xsd:nonNegativeInteger)
Wikipage revision ID	1068430390 (xsd:integer)
Link from a Wikipage to another Wikipage	Group (mathematics) Log semiring Projective linear group Undefined (mathematics) Unit interval Asymptote Monotone convergence theorem Radius of convergence Semigroup Calculus Real numbers Infinity Division by zero Dominated convergence theorem Metrizable space Power series Series (mathematics) Dedekind–MacNeille completion Compact space Construction of the real numbers Continuous function Homeomorphism Order topology Function (mathematics) IEEE 754 Identity function Improper integral Indeterminate form Extended natural numbers Field (mathematics) Infimum and supremum Infinity Absolutely integrable function Topology Total order Limit of a function Numerical analysis Mathematics Measure (mathematics) Neighbourhood (mathematics) Real number Riemann sphere Ring (mathematics) Singularity (mathematics)
has abstract	In mathematics, the affinely extended real number system is obtained from the real number system by adding two infinity elements: and where the infinities are treated as actual numbers. It is useful in describing the algebra on infinities and the various limiting behaviors in calculus and mathematical analysis, especially in the theory of measure and integration. The affinely extended real number system is denoted or or It is the Dedekind–MacNeille completion of the real numbers. When the meaning is clear from context, the symbol is often written simply as (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Extended_real_number_line
is Wikipage redirect of	+∞ -∞ Affine infinity Affinely extended real number line Affinely extended real number system Affinely extended real numbers Exended real Extended number Extended real Extended real line Extended real number Extended real number system Extended real numbers Extended reals Minus infinity Negative infinity −∞ Positive infinity Upper-extended real line
is Link from a Wikipage to another Wikipage of	Floating-point arithmetic Loeb space Log probability Log semiring NaN Number line 1 + 1 + 1 + 1 + ⋯ Absorbing element Actual infinity Addition Aleph number Approach space Arg max Moreau's theorem Bracket (mathematics)

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