Cryptocurrency Q&A
How do you prove something is not injective?
How do you prove something is not injective?
BonsaiVitality
Wed May 22 2024
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7 answers
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Could you please elaborate on the process of demonstrating that a function is not injective? Could you provide an example or two to illustrate the concept? I'm having some difficulty understanding how to conclusively show that a given function fails to be injective. Could you guide me through the steps of identifying a non-injective function and explaining the reasoning behind it? It would be helpful if you could also mention any common pitfalls or misconceptions that students tend to fall into when attempting to prove non-injectivity. Thank you for your assistance in clarifying this concept.
7 answers
Riccardo
Fri May 24 2024
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Andrea
Fri May 24 2024
To demonstrate that a function lacks injectivity, we must exhibit a specific instance. This involves finding elements within the domain that, despite their distinctiveness, map to the same value in the range.
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Bianca
Fri May 24 2024
Injectivity, in essence, demands that each input corresponds uniquely to an output. When this uniqueness is breached, the function ceases to be injective.
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AltcoinExplorer
Fri May 24 2024
Therefore, to negate the injectivity of a function, we must locate two distinct elements in the domain that share a common image under the function.
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Michele
Fri May 24 2024
Such an example suffices to prove non-injectivity, as it contradicts the requirement of unique mapping from domain to range.
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