mid
Denotes a conditional separator in set-builder notation, creating a clear division between a set's elements and their defining conditions.
Overview
Essential for writing mathematical sets in a formal and precise manner, particularly in set theory, logic, and abstract mathematics.
- Commonly used in set-builder notation to separate the set variable from its constraints
- Appears frequently in discrete mathematics and formal proofs
- Helps express complex set definitions clearly by distinguishing between the set elements and their properties
- Often encountered in advanced algebra, topology, and theoretical computer science when defining specific subsets or custom sets
Examples
Define a set using set-builder notation with a condition.
\{x \in \mathbb{R} \mid x > 0\}Specify a conditional probability.
P(A \mid B) = \frac{P(A \cap B)}{P(B)}Define a function's domain with multiple conditions.
\{x \in \mathbb{R} \mid x < -1 \text{ or } x > 1\}