Definition:Euler Diagram
Definition
An Euler diagram is a graphical technique for illustrating the relationships between sets.
It differs from a Venn diagram in that whereas the latter illustrates all possible intersections between a number of general sets, an Euler diagram depicts only those which are relevant for the situation being depicted.
Examples
The following examples show:
- $(\text a)$ The subset relation $T \subseteq S$
- $(\text b)$ Examples of disjoint sets $S \cap T = \O$
- $(\text c)$ The most general case: $S \cap T \ne \O$, $T \nsubseteq S$, $S \nsubseteq T$
The shape of the areas is irrelevant, but usually circles are used.
Also known as
Some sources refer to a Euler diagram as Euler's circles.
Note that the term Venn diagram is frequently encountered where Euler diagram would be more accurate.
Ultimately it doesn't really matter, as these diagrams have no greater purpose than to provide an illustrative clarification. They cannot be used for rigorous proof.
Also see
Source of Name
This entry was named for Leonhard Paul Euler.
Sources
- 1965: A.M. Arthurs: Probability Theory ... (previous) ... (next): Chapter $1$: Set Theory: $1.2$: Sets and subsets
- (where this is referred to as a Venn diagram)
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 1.2$.Subsets: Example $10$
- (where this is referred to as a Venn diagram)
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 2$: Sets and functions: Sets
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Euler's circles