Could you please explain to me what is meant by the term "not injective"? I'm having some difficulty grasping the concept, and I'd appreciate a clear and concise explanation. Could you possibly provide an example or two to illustrate the concept? Additionally, how does the lack of injectivity affect functions in general? I'm particularly interested in understanding its implications in the context of cryptocurrency and finance. Thank you for your assistance.
7 answers
BlockchainBaronessGuard
Sat May 25 2024
Understanding the concept of non-injectivity in functions is crucial for a comprehensive grasp of mathematical functions. To articulate this precisely, we must negate one of the equivalent versions of the definition of injectivity.
mia_harrison_painter
Fri May 24 2024
Injectivity, in essence, means that each input of a function uniquely determines its output. Conversely, non-injectivity occurs when multiple inputs map to the same output.
emma_carter_doctor
Fri May 24 2024
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Lorenzo
Fri May 24 2024
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Caterina
Fri May 24 2024
To illustrate, consider a function F that maps elements from a set to another set. If we can find two distinct elements, x and x', within the domain of F that have the same function value, F(x) = F(x'), then F is not injective.