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The term "Venn diagram" was later used by Clarence Irving Lewis in 1918, in his book A Survey of Symbolic Logic. [7] [13] In the 20th century, Venn diagrams were further developed. David Wilson Henderson showed, in 1963, that the existence of an n-Venn diagram with n-fold rotational symmetry implied that n was a prime number. [14]
The same method can also be illustrated with a Venn diagram as follows, with the prime factorization of each of the two numbers demonstrated in each circle and all factors they share in common in the intersection. The lcm then can be found by multiplying all of the prime numbers in the diagram. Here is an example: 48 = 2 × 2 × 2 × 2 × 3,
Venn diagram of information theoretic measures for three variables x, y, and z. Each circle represents an individual entropy : H ( x ) {\displaystyle H(x)} is the lower left circle, H ( y ) {\displaystyle H(y)} the lower right, and H ( z ) {\displaystyle H(z)} is the upper circle.
Venn diagrams are a more restrictive form of Euler diagrams. A Venn diagram must contain all 2 n logically possible zones of overlap between its n curves, representing all combinations of inclusion/exclusion of its constituent sets. Regions not part of the set are indicated by coloring them black, in contrast to Euler diagrams, where membership ...
Parts of these same circles are used to form the triquetra, a figure of three overlapping semicircles (each two of which form a vesica piscis symbol) that again has a Reuleaux triangle at its center; [76] just as the three circles of the Venn diagram may be interlaced to form the Borromean rings, the three circular arcs of the triquetra may be ...
As a human activity, the practice of mathematics has a social side, which includes education, careers, recognition, popularization, and so on. In education, mathematics is a core part of the curriculum and forms an important element of the STEM academic disciplines.
Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. [3] Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language.
An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes all the key components of the argument, traditionally called the conclusion and the premises , also called contention and reasons . [ 1 ]