TeXipedia

simcolon

Represents a relation symbol displaying a colon-like mark with a tilde above it, used in mathematical notation to indicate similarity or correspondence.

Overview

Primarily employed in advanced mathematical contexts where standard notation needs to be extended with additional relational symbols. This specialized symbol helps mathematicians and researchers:

  • Express nuanced relationships between mathematical objects
  • Denote specific types of correspondences or mappings
  • Distinguish from regular colon notation when additional meaning is needed

Most commonly found in abstract algebra, category theory, and theoretical mathematics where precise symbolic notation is essential.

Examples

Expressing a proportional relationship between variables.

x∼:yx \simcolon y 
x \simcolon y

Denoting a mapping or correspondence between sets.

f:A∼:Bf: A \simcolon B 
f: A \simcolon B

Indicating a ratio comparison in statistics.

observed∼:expected=3∼:2\text{observed} \simcolon \text{expected} = 3 \simcolon 2 
\text{observed} \simcolon \text{expected} = 3 \simcolon 2