EchoChaser
Thu May 23 2024
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6 answers
1565
How to prove something is injective?
Could you please elaborate on the methods used to demonstrate that a function is injective? Could you provide examples or step-by-step instructions to help me understand the process? Additionally, are there any specific properties or characteristics of injective functions that I should be aware of? Finally, how does proving injectivity differ from proving other mathematical properties like surjectivity or bijectivity?
BonsaiVitality
Wed May 22 2024
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7 answers
1610
How do you prove something is not injective?
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.
