Argument
Set (mathematics)
Overview
well-defined mathematical collection of distinct objects
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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Thus a momentary thing is a set of particulars, while a thing (which may be identified with the whole history of the thing) is a series of such sets of particulars. The particulars in one set are collected together by the laws of perspective; the successive sets are collected together by the laws of dynamics. This is the view of the world which is appropriate to traditional physics.
Bertrand Russell, The Analysis of Mind
Names Set several times; states what Set is.
Two sets of four points each are defined as having the same anharmonic ratio, when (1) each set of four lies in one straight line, and (2) corresponding points of different sets lie two by two on four straight lines through a single point, or when both sets have this relation to any third set[123]. And reciprocally: Two sets of four straight lines are defined as having the same anharmonic ratio when (1) each set of…
Bertrand Russell, An essay on the foundations of geometry
Names Set several times; states what Set is.
The importance of the equality of abstractive sets arises from the assumption that the intrinsic characters of the two sets are identical. If this were not the case exact observation would be at an end. It is evident that any two abstractive sets which are equal to a third abstractive set are equal to each other. An 'abstractive element' is the whole group of abstractive sets which are equal to any one of…
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
Names Set several times; states what Set is.
Philosophers who discussed Set (mathematics)
Related ideas
- Finite set
- Georg Cantor
- Tuple
- Infinite set
- Integer
- If and only if
- Zermelo–Fraenkel set theory
- Foundations of mathematics
- Ernst Zermelo
- Function (mathematics)
- Mathematics
- Mathematical object
- Rational number
- Real number
- Natural number
- Ordered pair
- Relation (mathematics)
- Domain of discourse
- Power set
- Set theory
- Total order
- Uncountable set
- Variable (mathematics)
- Singleton (mathematics)
Place in the tradition
Part of Coherentism.