Indizesfolge

Indizesfolge is a term that appears in the context of mathematics, particularly in set theory and logic. It refers to a sequence of indices. More formally, an indizesfolge can be understood as a function whose domain is a set of natural numbers (or an initial segment thereof) and whose codomain is another set, typically a set of sets or a set of elements from a larger structure. In essence, it's a way of systematically labeling or ordering elements of another set.

For example, if we have a collection of sets denoted by $A_1, A_2, A_3, \dots$, then the sequence $(A_i)_{i \in \mathbb{N}}$ is an indizesfolge. The term "indizesfolge" itself is German, translating directly to "index sequence" or "sequence of indices." The concept is fundamental when dealing with unions, intersections, or other operations on collections of mathematical objects that are indexed. Understanding indizesfolge is crucial for grasping concepts like indexed families and their properties in various mathematical fields.