Sunday, May 30, 2010

Does LaTeX Contain a "such that" Symbol?

The phrase such that is commonly used in mathematics to designate conditions that a statement is subject to. The handwritten symbol for such that is similar to a right parenthesis with a strikethrough and can be created using MathType thus,

such that symbol created with MathType

Math textbook often use a symbol similar to a backwards epsilon to represent such that but it is a flipped version of the symbol used to represent set membership. In LateX, a math typesetting language, the names for these symbols are \ni and \in respectively.

such that in a 1967 Addison-Wesley math book

People have tried to come up with ways to better represent such that in print. In TeX one can use a macro to combine a \ni with a horizontal line and this is used as a definition. LaTex apparently lacks this capability.

The current usage can potentially lead to confusion. The problem is that one is using a symbol from set theory to represent a control operator. One expression is subject to the control of another. This relationship suggests that the symbol used may be a simplified representation of a trident which was a symbol for power in the religion of ancient Greece. The trident as a symbol is directional and it is clear from context which expression exercises control. A parenthesis with strikethrough would therefore be a better symbol for such that.

Efforts are underway to develop a new version of LaTeX. Perhaps they could include strikeout text within a math statement so that one can create a unique such that symbol. From the computer science perspective it would be better to have a separate "entity," an amperstand-number combination, to designate a sideways trident like symbol for such that.

I should note that both MathType and Wolfram Alpha use a LaTeX \backepsilon or , Extended HTML entity &8717;, for such that. The entity corresponding to \ni or ∋ is ∋. (If you see square boxes instead of symbols, try viewing this page in another browser such as Google Chrome or Apple's Safari.)