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set of indiscernibles
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set of indiscernibles

mathematics
Also known as: homogeneous set
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In mathematics, the concept of "indiscernibles" relates to whether elements within a set can be distinguished from one another based on their properties. A set of indiscernibles is a collection of elements where a model cannot differentiate between them.1

This idea is connected to the principle of the identity of indiscernibles, which posits that if two objects share all their properties, they must be identical. Conversely, if they are not identical, they must differ in at least one property.2

In set theory, the principle of extension states that a set is defined by its members, not by how it's described. This means two sets are equal if they contain exactly the same elements. This principle is fundamental to understanding how sets are structured and compared in mathematics.3

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4 Britannica Sources
  1. metalogic - Ultrafilters , ultraproducts , and ultrapowers
  2. identity of indiscernibles
  3. set theory - Essential features of Cantorian set theory
  4. set theory - Equivalent sets

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