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Snake case (sometimes stylized autologically as snake_case) is the naming convention in which each space is replaced with an underscore (_) character, and words are written in lowercase. It is a commonly used naming convention in computing, for example for variable and subroutine names, and for filenames. One study has found that readers can ...
The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences.The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its applications, for instance in algebraic topology.
In computer programming, a naming convention is a set of rules for choosing the character sequence to be used for identifiers which denote variables, types, functions, and other entities in source code and documentation.
In the homological case, the differentials have bidegree (−r, r − 1), so they decrease n by one. In the cohomological case, n is increased by one. When r is zero, the differential moves objects one space down or up. This is similar to the differential on a chain complex.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
We say that intersects (meets) if there exists some that is an element of both and , in which case we also say that intersects (meets) at. Equivalently, A {\displaystyle A} intersects B {\displaystyle B} if their intersection A ∩ B {\displaystyle A\cap B} is an inhabited set , meaning that there exists some x {\displaystyle x} such that x ∈ ...
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.