analysis (differential/integral calculus, functional analysis, topology)
metric space, normed vector space
open ball, open subset, neighbourhood
convergence, limit of a sequence
compactness, sequential compactness
continuous metric space valued function on compact metric space is uniformly continuous
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The real numbers as encountered in prealgebra.
Let be an Archimedean integral domain and let be the unit interval in . Let be a sequence of decimal digits, where is the set of all natural numbers , and let be the canonical embedding of into . The prealgebra real numbers is the initial Archimedean integral domain such that for every such sequence , the sequence
has a limit in the unit interval .
If the limited principle of omniscience is true, then every Cauchy real number is a prealgebra real number.
Last revised on June 10, 2022 at 00:15:16. See the history of this page for a list of all contributions to it.