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Hi I'm in grade 10 and I'm doing nested intervals. Under my current circumstances I am unable to have a teacher, so I'm self teaching with the help of textbooks. I understand very, very basic intervals, but I've come to a question where it wants to know if the intervals can be nested and I don't how simple this is but if anyone can break it down that would be extremely helpful!

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Maddy. P
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  • A set of nested intervals is an ordered sequence of intervals $I_1, I_2, ..., I_n,..$ such that $I_1 \supseteq I_2$, $I_2 \supseteq I_3$ and ... $I_n \supseteq I_{n+1}$.. and so on. List does not necessarily need to be infinite. We might be able to help you better if you share your problem?? And.. https://www.projectrhea.org/rhea/images/thumb/4/44/Countability_fig3_mh.jpeg/400px-Countability_fig3_mh.jpeg – Ishfaaq Sep 01 '14 at 14:30

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A sequence of intervals $I_1,I_2,\ldots$ is nested if $I_1 \supset I_2 \ldots$. In other words, the later intervals all lie within the previous ones.

StrangerLoop
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