116 lines
2.0 KiB
Markdown
116 lines
2.0 KiB
Markdown
---
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title: "Almost"
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chunk: 1/1
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source: "https://en.wikipedia.org/wiki/Almost"
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category: "reference"
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tags: "science, encyclopedia"
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date_saved: "2026-05-05T07:23:11.268039+00:00"
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instance: "kb-cron"
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---
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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 on the context, and may mean "of measure zero" (in a measure space), "finite" (when infinite sets are involved), or "countable" (when uncountably infinite sets are involved).
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For example:
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The set
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S
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=
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{
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n
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∈
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N
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n
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≥
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k
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}
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{\displaystyle S=\{n\in \mathbb {N} \,|\,n\geq k\}}
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is almost
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N
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{\displaystyle \mathbb {N} }
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for any
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k
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{\displaystyle k}
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in
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N
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{\displaystyle \mathbb {N} }
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, because only finitely many natural numbers are less than
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k
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{\displaystyle k}
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.
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The set of prime numbers is not almost
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N
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{\displaystyle \mathbb {N} }
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, because there are infinitely many natural numbers that are not prime numbers.
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The set of transcendental numbers are almost
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R
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{\displaystyle \mathbb {R} }
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, because the algebraic real numbers form a countable subset of the set of real numbers (which is uncountable).
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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.
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== See also ==
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Almost periodic function - and Operators
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Almost all
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Almost surely
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Approximation
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List of mathematical jargon
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== References == |