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2. Continuous or discrete variable - Wikipedia

   en.wikipedia.org/wiki/Continuous_or_discrete...

   In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively. [1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval. [2]

3. Cardinality of the continuum - Wikipedia

   en.wikipedia.org/wiki/Cardinality_of_the_continuum

   (This is true even in the case the expansion repeats, as in the first two examples.) In any given case, the number of decimal places is countable since they can be put into a one-to-one correspondence with the set of natural numbers . This makes it sensible to talk about, say, the first, the one-hundredth, or the millionth decimal place of π.

4. List of types of numbers - Wikipedia

   en.wikipedia.org/wiki/List_of_types_of_numbers

   Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.

5. First-countable space - Wikipedia

   en.wikipedia.org/wiki/First-countable_space

   In topology, a branch of mathematics, a first-countable space is a topological space satisfying the "first axiom of countability". Specifically, a space X {\displaystyle X} is said to be first-countable if each point has a countable neighbourhood basis (local base).

6. Continuum (set theory) - Wikipedia

   en.wikipedia.org/wiki/Continuum_(set_theory)

   If [A,B] is a cut of C, then either A has a last element or B has a first element. (compare Dedekind cut) There exists a non-empty, countable subset S of C such that, if x,y ∈ C such that x < y, then there exists z ∈ S such that x < z < y. (separability axiom) C has no first element and no last element.

7. Computable number - Wikipedia

   en.wikipedia.org/wiki/Computable_number

   A real number is computable if its digit sequence can be produced by some algorithm or Turing machine. The algorithm takes an integer as input and produces the -th digit of the real number's decimal expansion as output. (The decimal expansion of a only refers to the digits following the decimal point.)