👉 In mathematics, a homomorphism is a function that preserves the structure of the domain and codomain. It means that for any two functions f and g from one set X to another set Y, if they both have the same domain (the set of input values), then their composition f ∘ g also has the same domain. This property allows us to apply certain operations or transformations to a function without changing its output. For example: 1. If f is a homomorphism from R
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What is the definition of Homomorphism? 🙋
👉 A homomorphism, also known as a bijective map, is a function that preserves the properties of both its domain and codomain. Specifically, it must satisfy the following conditions:
1.
Identity
: For every element \(a\) in the domain, there exists an element \(b\) in the codomain such that \(ba = ab\). This means that for any element \(a\) in the domain, there is a unique element \(b\) in the codomain such that \(
