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2. List of types of numbers - Wikipedia

   en.wikipedia.org/wiki/List_of_types_of_numbers

   Computable number: A real number whose digits can be computed by some algorithm. Period: A number which can be computed as the integral of some algebraic function over an algebraic domain. Definable number: A real number that can be defined uniquely using a first-order formula with one free variable in the language of set theory.

3. Real number - Wikipedia

   en.wikipedia.org/wiki/Real_number

   The long real line pastes together ℵ 1 * + ℵ 1 copies of the real line plus a single point (here ℵ 1 * denotes the reversed ordering of ℵ 1) to create an ordered set that is "locally" identical to the real numbers, but somehow longer; for instance, there is an order-preserving embedding of ℵ 1 in the long real line but not in the real ...

4. Construction of the real numbers - Wikipedia

   en.wikipedia.org/wiki/Construction_of_the_real...

   An axiomatic definition of the real numbers consists of defining them as the elements of a complete ordered field. [2] [3] [4] This means the following: The real numbers form a set, commonly denoted , containing two distinguished elements denoted 0 and 1, and on which are defined two binary operations and one binary relation; the operations are called addition and multiplication of real ...

5. Multiplication - Wikipedia

   en.wikipedia.org/wiki/Multiplication

   Systematic generalizations of this basic definition define the multiplication of integers (including negative numbers), rational numbers (fractions), and real numbers. Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have some given lengths.

6. Arithmetic - Wikipedia

   en.wikipedia.org/wiki/Arithmetic

   Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational ...

7. Addition - Wikipedia

   en.wikipedia.org/wiki/Addition

   The sum of real numbers a and b is defined element by element: Define + = {+,}. [65] This definition was first published, in a slightly modified form, by Richard Dedekind in 1872. [66] The commutativity and associativity of real addition are immediate; defining the real number 0 to be the set of negative rationals, it is easily seen to be the ...