ALEF SYMBOL by ℵancym

alefsym.adoc

ALEF SYMBOL by ℵancym

^Updated 2015-02-19; first published 2014-11-01; feedback welcome.^[1]^

What is Aleph?

The character Aleph (ℵ), which is also spelled Alef, is used:

1. in Mathematics, to represent different levels of infinity. ℵ₀ is the smallest level of infinity, ℵ₁ is the next level, etc.^[2][3]

2. in Hebrew, to represent

   • the first letter of the alphabet,

   • the number one (in some contexts), and

   • the oneness of God (in Jewish mysticism).

Where is Aleph in the Unicode character set?

In Unicode, which is a standard universal character set that can support over a million characters^[4], the mathematical and Hebrew meanings of Aleph are represented by two different characters:

1. ALEF SYMBOL (U+2135), which is in the Letterlike Symbols Unicode block

2. HEBREW LETTER ALEF (U+05D0), which is in the Hebrew Unicode block

The main difference between these is that ALEF SYMBOL is part of a left-to-right directionality character set and HEBREW LETTER ALEF is part of a right-to-left directionality character set. ALEF SYMBOL is a compatibility character and these two characters are considered border-line semantically distinct. It is common to use these characters interchangeably, especially when using a font that supports only one of them.

How to use Aleph in your writing

To include Aleph in a document, you need a method for inserting it into your document’s markup.^[5] Possible methods include:

• Insert the actual UTF-8^[6] encoded ALEF SYMBOL Unicode character by, for example, copying and pasting it from FileFormat.Info/info/unicode/char/2135/browsertest.htm.

• Insert the actual UTF-8 encoded HEBREW LETTER ALEF Unicode character by, for example, copying and pasting it from FileFormat.Info/info/unicode/char/05d0/browsertest.htm.

• Insert a named character reference that is supported by your markup language. For example, in LaTeX you can insert the string \aleph and in HTML you can insert the string ℵ.

• Insert a numeric character reference that is supported by your markup language. Examples are in the tables below.

• Insert an image of the character.

The two tables below list some ways to insert these characters. You can use the third column of these tables to see how the web browser you are using right now supports these different markup methods.

Note

The appearance of the Aleph characters in the third column of the tables below depends on the fonts that are installed on your system. If your system does not support a font that contains a character, you will see an empty box or a question mark. If ALEF SYMBOL and HEBREW LETTER ALEF look different from how they look at the FileFormat.Info links above, your browser may be doing font substitution.

 

Table 1. ALEF SYMBOL

HTML[7] Markup Method	Markup code	Rendered in your browser
named character reference	ℵ	ℵ
decimal numeric character reference	ℵ	ℵ
hexadecimal numeric character reference	ℵ	ℵ
actual UTF-8 encoded ALEF SYMBOL	copied & pasted from here	ℵ

   

Table 2. HEBREW LETTER ALEF

HTML Markup Method	Markup code	Rendered in your browser
named character reference	n/a	n/a
decimal numeric character reference	א	א
hexadecimal numeric character reference	א	א
actual UTF-8 encoded HEBREW LETTER ALEF	copied & pasted from here	א

My relationship with Aleph

The Aleph character is meaningful to me because I love Mathematics, the infinite, and the mystical aspects of reality. I’ve also been interested in fonts and character sets ever since I was a Mathematics graduate student and created^[8] my own mathematical fonts while writing my thesis about the Axiom of Choice.^[3] Because of the link between the Aleph character and my interests, I’ve created a new identity for myself named AlefSym, which I plan to use only for my own writing. This identity’s avatar is ℵ and tagline is:

AlefSym by ℵancym

It’s nice that it rhymes and that ℵ looks like my initial N 😌.

I’m thinking about changing the avatar of my nancym.tumblr.com and twitter.com/@nm identities to ℵ₁ to tie these aspects of my personality together. ℵ is just me and ℵ₁ is me plus the things I reblog and retweet, which is a big jumbled uncountable mess of almost everything in the universe.

   

Resources

• https://en.wikipedia.org/wiki/Aleph_(disambiguation)

• https://en.wikipedia.org/wiki/Aleph

• https://en.wikipedia.org/wiki/Aleph_number

• https://en.wikipedia.org/wiki/Georg_Cantor

• http://mathoverflow.net/questions/162844/aleph-looks-like-mathbb-n (includes history of Cantor’s choice of Aleph)

 

Footnotes

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1. You can ✭ or comment on this article on its permalink pages at Gist, Tumblr, and Twitter.

2. In 1874 Cantor showed that there is more than one level of infinity and started using ℵ, followed by a subscript, to represent different levels of infinity.

3. If the Axiom of Choice is false, it is possible there are infinities other than the Alephs {ℵ₀, ℵ₁, ℵ₂, …​, ℵ_ω, ℵ_ω+1, …​}.

4. It’s more correct to say Unicode can support over a million "code points" (rather than "characters"). U+2135 and U+05D0 are examples of Unicode code points.

5. Common markup languages include AsciiDoc, HTML, LaTeX, Markdown, SGML, XHTML, and XML. AsciiDoc and Markdown are known as "lightweight markup languages."

6. UTF-8 is the encoding I’m using on this web page (and the encoding that is used on most web pages nowadays).

7. By "HTML," I mean HTML and lightweight HTML markup languages, such as AsciiDoc and Markdown. I wrote this article in AsciiDoc.

8. In graduate school, I spent many hours using Fontastic to create mathematical fonts while procrastinating writing my thesis. For example, I fiddled a lot with the pixels in my 2^ℵ₀ character.