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alefsym

Represents the first transfinite cardinal number in set theory and mathematics, denoting the size of countably infinite sets.

Overview

A fundamental symbol in mathematical set theory and logic that represents the cardinality of the natural numbers and other countably infinite sets.

  • Essential in discussions of infinite sets and cardinal arithmetic
  • Commonly used when discussing the continuum hypothesis
  • Appears frequently in advanced mathematics, particularly in set theory proofs and discussions of infinity
  • Often encountered in theoretical computer science when discussing algorithmic complexity and countable sets

Examples

Denoting the cardinality of the set of real numbers.

∣R∣=ℵ\left|\mathbb{R}\right| = \alefsym 
\left|\mathbb{R}\right| = \alefsym

Comparing infinite set cardinalities.

∣N∣<∣R∣=ℵ1|\mathbb{N}| < |\mathbb{R}| = \alefsym_1 
|\mathbb{N}| < |\mathbb{R}| = \alefsym_1

Expressing the continuum hypothesis.

2ℵ0=ℵ12^{\alefsym_0} = \alefsym_1 
2^{\alefsym_0} = \alefsym_1