Generally, a semi-infinite set is bounded in one direction, and unbounded in another.
For instance, the natural numbers are semi-infinite considered as a subset of the integers; similarly, the intervals
Semi-infinite regions occur frequently in the study of differential equations.
[2][3] For instance, one might study solutions of the heat equation in an idealised semi-infinite metal bar.
[4] Most forms of semi-infiniteness are boundedness properties, not cardinality or measure properties: semi-infinite sets are typically infinite in cardinality and measure.