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In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures. For instance, a vector space involves a second structure called a field, and an operation called scalar multiplication between elements of the field (called scalars), and elements of the vector space (called vectors).
In mathematics, many types of algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures may be viewed in different ways, however the common starting point of algebra texts is that an algebraic object incorporates one or more sets with one or more binary operations or unary operations satisfying a ...
The General Certificate of Secondary Education (GCSE) is an academic qualification in a range of subjects taken in England, Wales, and Northern Ireland, having been introduced in September 1986 and its first exams taken in 1988.
A structure on a set, or more generally a type, consists of additional mathematical objects that in some manner attach (or are related) to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance.
Please help by editing the article to make improvements to the overall structure. ( February 2024 ) ( Learn how and when to remove this message ) This is a list of notable theorems .
She said her mother took her back to the eye doctor. That's when the family was told their child had "behavioral problems," SWNS reported. They were eventually referred to two different hospitals.
This reflects also an informal way of thinking: that the group is the same as the set except that it has been enriched by additional structure provided by the operation. For example, consider the set of real numbers R {\displaystyle \mathbb {R} } , which has the operations of addition a + b {\displaystyle a+b} and multiplication a b ...