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For questions requesting examples of a certain structure or phenomenon
0
votes
Nontrivial question about Fibonacci numbers?
Ask them to prove that the ratios of the Fibonacci sequence tends to the golden ratio. That is $\frac{F_n}{F_{n-1}} \to \phi$. This can be done with basic calculus.
1
vote
What are your favorite instructional counterexamples?
Another one of my favorite counter examples is $2\mathbb{Z}$ which is a RNG, or a ring without identity. …
6
votes
What are your favorite instructional counterexamples?
This was one of the first counter-examples in a research paper that I understood because the authors method of proof is very elementary. …