abstractmath.org GLOSSARY
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pairwise disjoint
partition
The word partition has several distinct meanings in math.
¨ A partition of a set into disjoint blocks (same as an equivalence relation).
¨ A partition of an integer, expressing the integer as a sum of integers.
¨ A partition of an interval, used in the theory of integration.
¨ A partition of unity of a topological space.
All of these ideas involve the concept of breaking something up into distinct pieces, but they are genuinely distinct ideas.
permutation
Permutation is defined in
the literature in two different ways:
¨ A permutation of an n-element set is a sequence of length n in which each element of the set appears once. This is discussed in detail in Mathworld.
¨ A permutation of a set is a bijection from the set
to itself.
Of course, the two definitions can
be converted into each other, but psychologically they are rather different. The
discussion in Wikipedia gives both
definitions.
positive
In most texts and university courses, the phrase " x is positive" means x >
0. In a few texts and in .
Acknowledgment
The members of the RUME discussion list.
pons asinorum
power
The integer 125 is a power of
prime
To be written
proper
¨ If a subset T of
a set S is not S, then it is a proper subset of S. (See also here.) This is also used with substructures of a
structure (proper subgroup, and so on).
¨ Some authors require that a proper subset of S be not only not all of S but also not be empty. Unless the author
makes it clear, you cannot
tell which is
meant.
¨ The word proper is also used by some authors to mean
nontrivial; for example, a proper automorphism would be a
non-identity automorphism.