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What is Almost mean?
In set theory, when dealing with sets of infinite size, the term almost or nearly is used to refer to all but a negligible amount of elements in the set. The notion of "negligible" depends in the context, and may mean "of measure zero" (in a measure space), "countable" (when uncountably infinite sets are involved), or "finite" (when infinite sets are involved).
For example:
The set S = { n ∈ N | n ≥ k } {\displaystyle S=\{n\in \mathbb {N} \,|\,n\geq k\}} is almost N {\displaystyle \mathbb {N} } for any k {\displaystyle k} in N {\displaystyle \mathbb {N} } , because only finitely many natural numbers are less than k {\displaystyle k} .The set of prime numbers is not almost N {\displaystyle \mathbb {N} } , because there are infinitely many natural numbers that are not prime numbers.The set of transcendental numbers are almost R {\displaystyle \mathbb {R} } , because the algebraic real numbers form a countable subset of the set of real numbers (which is uncountable).The Cantor set is uncountably infinite, but has Lebesgue measure zero. So almost all real numbers in (0, 1) are members of the complement of the Cantor set. referenceFull Form | Category |
---|---|
Above Mentioned | General |
Amperes Per Meter | General |
Almost | Internet |
Approach and Moor | Military and Defence |
Posted on 30 Apr 2022, this text provides information on Miscellaneous in Internet related to Internet. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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