What is a small set arranged within a larger set called?

The correct term for a small set that is arranged within a larger set is "subset." In set theory, a subset is defined as a set whose elements are all contained within another set, often referred to as the superset.

For example, if you have a set of all integers, a subset could be the set of all even integers, as all even integers exist within the larger set of all integers.

The term "inset" generally refers to a smaller image or a region of a visual context and is not commonly used in set theory. "Contextual set" and "focus set" do not have standard definitions within set theory and may vary in meaning depending on the context in which they are used, making them less suitable for this question. Thus, "subset" is the most appropriate term to indicate a small set within a larger set.