# Real Numbers

### Some articles on real numbers, numbers, real number, number:

Albert Algebra
... the study of non-associative algebras, usually working over the real numbers ... Over the real numbers, there are two such Jordan algebras up to isomorphism ... example, if we complexify the two Albert algebras over the real numbers, we obtain isomorphic Albert algebras over the complex numbers ...
Complex Numbers Exponential - Powers of Complex Numbers - Failure of Power and Logarithm Identities
... Some identities for powers and logarithms for positive real numbers will fail for complex numbers, no matter how complex powers and complex logarithms are defined as single-valued ... For example The identity log(bx) = x · log b holds whenever b is a positive real number and x is a real number ... identities (bc)x = bxcx and (b/c)x = bx/cx are valid when b and c are positive real numbers and x is a real number ...
Times - Multiplication of Different Kinds of Numbers
... Numbers can count (3 apples), order (the 3rd apple), or measure (3.5 feet high) as the history of mathematics has progressed from counting on our fingers to modelling quantum mechanics ... Integers is the sum of M copies of N when N and M are positive whole numbers ... This gives the number of things in an array N wide and M high ...
Real Number - Generalizations and Extensions
... The real numbers can be generalized and extended in several different directions The complex numbers contain solutions to all polynomial equations and hence are an algebraically closed field unlike ... However, the complex numbers are not an ordered field ... The affinely extended real number system adds two elements +∞ and −∞ ...
Complete Quotients and Equivalent Real Numbers - An Equivalence Relation Defined By LFTs
... We can define an equivalence relation on the set of real numbers by means of this group of linear fractional transformations ... We will say that two real numbers x and y are equivalent (written x ~ y) if for some integers a, b, c, and d such that ad − bc = ±1 ... and it can be used to separate the real numbers into equivalence classes ...

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