Math Font, Unicode, Gothic Letters, Double Struck

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Math Font, Unicode, Gothic Letters, Double Struck

Xah Lee, 2010-12-12

This post is some thoughts and info about specially styled alphabets used in math, fonts, unicode.

In math, there's these special styled letters:

  • Double Struck: ℂ ℍ ℕ ℙ ℚ ℝ ℤ ⅆ ⅇ ⅈ ⅉ
  • Gothic: ℭ ℑ ℌ ℜ ℨ
  • Scripted ℬ ℰ ℱ ℋ ℐ ℒ ℳ ℘ ℛ ℯ ℓ ℊ ℴ

Note that the above does not contain the full alphabets A to z. The above chars are in Unicode' “Basic Multilingual Plane”. (BMP. Their unicode number can be expressed by 4 digits of hexadecimal. (See also: UNICODE Basics: What's Character Encoding, UTF-8, and All That?)) The full set of letters from A to z of these styles is also in unicode, but is outside of BMP, thus are currently not widely supported. (meaning, you'll need to install special math fonts to see them.) If you are using latest versions of browsers (as of 2010-12), all the above letter forms should show up correctly. In particular, Google Chrome (8.0), Firefox (3.6.12), Opera (10.63), or Safari (5.0.3), Internet Explorer 8, all display them fine. (If they don't show up in your browser, and you are using latest version, see: Unicode Character Shows Blank, Question Mark, Gibberish and Best Fonts for Unicode )

Here's a exampe of the complete set of gothic styled latin alphabets:

Capitals: 𝔄 𝔅 ℭ 𝔇 𝔈 𝔉 𝔊 ℌ ℑ 𝔍 𝔎 𝔏 𝔐 𝔑 𝔒 𝔓 𝔔 ℜ 𝔖 𝔗 𝔘 𝔙 𝔚 𝔛 𝔜 ℨ

Lowercase: 𝔞 𝔟 𝔠 𝔡 𝔢 𝔣 𝔤 𝔥 𝔦 𝔧 𝔨 𝔩 𝔪 𝔫 𝔬 𝔭 𝔮 𝔯 𝔰 𝔱 𝔲 𝔳 𝔴 𝔵 𝔶 𝔷

To display the above, you'll need to install the STIX Fonts. It's a font set specially designed for math. Home page is at stixfonts.org. After you install the font, you can choose “StixGeneral”. (be sure to follow the instruction on Windows. You can't just drop the font in the font folder)

The Gothic styled letters is also known as “Blackletter”. The Double Struck (ℝ ℂ) is also known as “Blackboard bold”. I don't like the term Blackboard Bold, and the “double struck” should be “double stroke”.

In Unicode, besides the sets of gothic, double struck, scripted, forms for the whole latin alphabet, there's also slanted and bold and “slanted and bold” variants, as actual unicode chars. They are all outside of BMP. You can see them at Mathematical Alphanumeric Symbols. I would advise to not use these stylistic variants as much as possible. Using slanted letter for variables in math is not semantically meaningful, in works such as Calculational Proofs notation or computer proof and computer algebra languages. Slanted letters as variables contribute to the problem of traditional math notation. The essential reason it's bad is because in traditional math notation, or the use of slanted font for variable, it basically treats the notation as visual glyphs of ideas, not as a language with structure and grammar. See:

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