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Inset theory, when dealing withsets ofinfinite size, the termalmost ornearly 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 ameasure space), "finite" (when infinite sets are involved), or "countable" (whenuncountably infinite sets are involved).

For example:

• The set${\displaystyle S=\{n\in \mathbb{N}|n\ge k\}}$ is almost${\displaystyle \mathbb{N}}$ for any${\displaystyle k}$ in${\displaystyle \mathbb{N}}$, because only finitely manynatural numbers are less than${\displaystyle k}$.
• The set ofprime numbers is not almost${\displaystyle \mathbb{N}}$, because there are infinitely many natural numbers that are not prime numbers.
• The set oftranscendental numbers are almost${\displaystyle \mathbb{R}}$, because thealgebraicreal numbers form acountablesubset of the set of real numbers (which is uncountable).^[1]
• TheCantor set is uncountably infinite, but hasLebesgue measure zero.^[2] So almost all real numbers in (0, 1) are members of thecomplement of the Cantor set.

Look upalmost in Wiktionary, the free dictionary.

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