What ℶ means
It labels beth numbers in a hierarchy of infinite sizes.
The beth hierarchy begins with a base size. At each successor stage—the step immediately after another stage—it takes the size of the previous set’s power set, or all its subsets. This tracks one way infinite sizes grow, alongside the aleph hierarchy, which orders infinite cardinalities.
The earliest credited use of beth notation is in Charles Sanders Peirce’s letter to Georg Cantor in December 1900. The notation seems to have fallen out of use, then was back in mathematical use by the 1950s.
Is ℶ the Hebrew letter ב?
No. ℶ is mathematical notation; ב is a Hebrew letter.
ℶ borrows the name and shape of Hebrew bet, but it serves a mathematical purpose. Formulas use ℶ as a left-to-right symbol; ב belongs in right-to-left Hebrew writing.
Formal and specialist: it signals set theory, logic, or advanced mathematical writing.
Using it as Hebrew text can change both the character and the text direction.
Part of the collection
What it means when someone sends it to you
4 readingsThe starting cardinal in the beth hierarchy.
Don't confuse it with
1
Related characters
3
Combination ideas
4Questions people ask
1Does ℶ₁ always equal ℵ₁?
No. ℶ₁ is the size of the real numbers. It equals ℵ₁ only under the continuum hypothesis, which says no infinite size lies between countable infinity and the real numbers.
More like this
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How to type or find ℶ
- Also called
- beth · beth number · beth notation
- Search it as
- set theory · power set · infinite cardinal · cardinality · aleph beth · beth LaTeX
- Shows up in
- Anything that takes text · its shape is whatever your font draws
ℶ\2136unicode-math, type \beth; its symbol table maps the command to ℶ.Codes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.