Concept
Disjoint sets
Overview
In set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two or more sets is called disjoint if any two distinct sets of the collection are disjoint.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
But, while a series of mathematical points arranged in empty space expresses fairly well the process by which we form the idea of number, these mathematical points have a tendency to develop into lines in proportion as our attention is diverted from them, as if they were trying to reunite with one another. And when we look at number in its finished state, this union is an accomplished fact: the points have become…
Henri Bergson, Time and Free Will
Close in meaning to Disjoint sets; the term itself is not named.
Propositions in which the assertion is not dependent on a condition, are said, in the language of logicians, to be _categorical_.
John Stuart Mill, A System of Logic
States what Disjoint sets is.
131. THIRDLY, it is, I think, an axiom universally received that quantities of the same kind may be added together and make one entire sum. Mathematicians add lines together: but they do not add a line to a solid, or conceive it as making one sum with a surface: these three kinds of quantity being thought incapable of any such mutual addition, and consequently of being compared together in the several ways of…
George Berkeley, An Essay Towards a New Theory of Vision
Close in meaning to Disjoint sets; the term itself is not named.
Related ideas
- Finite set
- Infinite set
- Function (mathematics)
- Mathematics
- Real number
- Intersection (set theory)
- Power set
- Set (mathematics)
- Set theory
- Topology
- Logic
- Union (set theory)
- Equivalence relation
- Empty set
Place in the tradition
Part of Intuitionistic logic.