symmetric monoidal (∞,1)-category of spectra
transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
For an abelian group and a pair of elements, their difference is the element
This is often considerd for the case that is the abelian group underlying a vector space , which which case one typically denotes the elements instead as and their difference as
Specifically if is the real line or the rational numbers of just the integers, one just writes . Etc.
For a commutative semigroup or magma and a pair of elements, their difference, if it exists, is an element such that
is called the subtrahend of and is called the minuend of .
For example, in the ordered commutative semigroup of positive integers , two positive integers have a difference if .
If the magma is a multiplicative monoid of a commutative ring, then the difference is usually called a quotient (see divisor (ring theory).
A commutative quasigroup is a commutative magma such that every pair of elements has a difference.
A derivative is a limiting ratio of differences.
Last revised on May 19, 2021 at 17:25:35. See the history of this page for a list of all contributions to it.