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2. 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.

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. First-countable space - Wikipedia

   en.wikipedia.org/wiki/First-countable_space

   Also, if is a function on a first-countable space, then is continuous if and only if whenever , then () (). In first-countable spaces, sequential compactness and countable compactness are equivalent properties. However, there exist examples of sequentially compact, first-countable spaces that are not compact (these are necessarily not ...

5. 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]

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. Sequential space - Wikipedia

   en.wikipedia.org/wiki/Sequential_space

   is the quotient of a first-countable space. X {\displaystyle X} is the quotient of a metric space. By taking Y = X {\displaystyle Y=X} and f {\displaystyle f} to be the identity map on X {\displaystyle X} in the universal property, it follows that the class of sequential spaces consists precisely of those spaces whose topological structure is ...

8. Real number - Wikipedia

   en.wikipedia.org/wiki/Real_number

   In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. [a] Every real number can be almost uniquely represented by an infinite decimal expansion. [b] [1]

9. Continuum (measurement) - Wikipedia

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

   In physics, for example, the space-time continuum model describes space and time as part of the same continuum rather than as separate entities. A spectrum in physics, such as the electromagnetic spectrum, is often termed as either continuous (with energy at all wavelengths) or discrete (energy at only certain wavelengths).