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  • https://math.libretexts.org/Bookshelves/Analysis/Introduction_to_Mathematical_Analysis_I_(Lafferriere_Lafferriere_and_Nguyen)/01%3A_Tools_for_Analysis/1.05%3A_The_Completeness_Axiom_for_the_Real_Numbers
    It follows that a set A is bounded if and only if there exist MR such that |x|M for all xA (see Exercise 1.5.1) \(x \leq \alpha \text { for all } x \in A...It follows that a set A is bounded if and only if there exist MR such that |x|M for all xA (see Exercise 1.5.1) xα for all xA (that is, α is an upper bound of A); xβ for all xA (that is, β is a lower bound of A); Prove that a subset A of R is bounded if and only if there is MR such that |x|M for all xA.
  • https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/An_Inquiry-Based_Approach_to_Abstract_Algebra_(Ernst)/03%3A_Subgroups_and_Isomorphisms/3.02%3A_Subgroup_Lattices
    One of the goals of this section is to gain better understanding of the structure of groups by studying their subgroups.

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