Cryptocurrency Q&A
What is the logical definition of injective?
What is the logical definition of injective?
CharmedEcho
Tue Oct 15 2024
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6 answers
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I'm trying to understand the concept of injective in a logical way. I want to know the precise definition that captures the essence of what it means for a function to be injective.
6 answers
HanRiverVisionary
Thu Oct 17 2024
Injectivity is a crucial property in various mathematical and computational contexts, including cryptography, coding theory, and algorithm design. It ensures that information is preserved and can be uniquely recovered, preventing issues like collisions or ambiguity.
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lucas_clark_artist
Thu Oct 17 2024
Specifically, a function f:A→B is injective if, for any two elements x and y in the domain A, the equality of their function values, f(x)=f(y), necessarily implies that the original elements themselves are equal, i.e., x=y.
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SakuraBlooming
Thu Oct 17 2024
This property ensures that each element in the domain A is uniquely mapped to a single element in the codomain B, without any overlap or ambiguity. In other words, no two distinct elements in A can have the same image under f.
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CryptoKnight
Thu Oct 17 2024
An alternative way to understand injectivity is through its contrapositive formulation. Here, the negation of the implication is considered: if x and y are not equal (x≠y), then their function values under f must also be distinct (f(x)≠f(y)).
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Bianca
Thu Oct 17 2024
The concept of an injective function, also known as a one-to-one function or denoted as 1-1, is a fundamental property in mathematics. It defines a special relationship between the domain A and the codomain B of a function f.
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