Two or more people who interact with each other to accomplish certain goals or meet certain needs
The definition you provided is not math-related, but rather relates to the concept of group or teamwork
The definition you provided is not math-related, but rather relates to the concept of group or teamwork. In mathematics, a group refers to a specific mathematical structure that consists of a set of elements combined with an operation that satisfies certain properties.
In group theory, a group is defined as a set G together with an operation (often denoted by *) that combines any two elements of G to produce another element in G. To be a group, this operation must satisfy the following properties:
1. Closure: For any two elements a and b in G, the result of the operation a * b also belongs to G.
2. Associativity: For any three elements a, b, and c in G, the result of the operation (a * b) * c is the same as a * (b * c).
3. Identity: There exists an identity element in G, denoted by e, such that for any element a in G, the operation a * e = a = e * a.
4. Inverse: For every element a in G, there exists another element b in G, denoted by a⁻¹, such that a * a⁻¹ = e = a⁻¹ * a.
These four properties collectively define a group. Groups can have various properties and may be classified based on these properties—such as finite or infinite, abelian or non-abelian, and more. The study of groups and their properties is an important branch of mathematics known as group theory.
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