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2. Category:Theorems about real number sequences - Wikipedia

   en.wikipedia.org/wiki/Category:Theorems_about...

   Pages in category "Theorems about real number sequences" The following 5 pages are in this category, out of 5 total. This list may not reflect recent changes. B.

3. Lambek–Moser theorem - Wikipedia

   en.wikipedia.org/wiki/Lambek–Moser_theorem

   If () is the prime-counting function (the number of primes less than or equal to ), then the th non-prime (1 or a composite number) is given by the limit of the sequence [7], + (), + (+ ()), … For some other sequences of integers, the corresponding limit converges in a fixed number of steps, and a direct formula for the complementary sequence ...

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. Continuum (set theory) - Wikipedia

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

   The cardinality of the continuum is the size of the set of real numbers. The continuum hypothesis is sometimes stated by saying that no cardinality lies between that of the continuum and that of the natural numbers , ℵ 0 {\displaystyle \aleph _{0}} , or alternatively, that c = ℵ 1 {\displaystyle {\mathfrak {c}}=\aleph _{1}} .

6. Baire space (set theory) - Wikipedia

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

   The basic open sets of the product topology are cylinder sets.These can be characterized as: If any finite set of natural number coordinates I={i} is selected, and for each i a particular natural number value v i is selected, then the set of all infinite sequences of natural numbers that have value v i at position i is a basic open set.

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