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  2. Upper and lower bounds - Wikipedia

    en.wikipedia.org/wiki/Upper_and_lower_bounds

    For example, 5 is a lower bound for the set S = {5, 8, 42, 34, 13934} (as a subset of the integers or of the real numbers, etc.), and so is 4. On the other hand, 6 is not a lower bound for S since it is not smaller than every element in S. 13934 and other numbers x such that x ≥ 13934 would be an upper bound for S.

  3. Coin problem - Wikipedia

    en.wikipedia.org/wiki/Coin_problem

    Frobenius coin problem with 2-pence and 5-pence coins visualised as graphs: Sloping lines denote graphs of 2x+5y=n where n is the total in pence, and x and y are the non-negative number of 2p and 5p coins, respectively. A point on a line gives a combination of 2p and 5p for its given total (green).

  4. Nested intervals - Wikipedia

    en.wikipedia.org/wiki/Nested_intervals

    The construction follows a recursion by starting with any number , that is not an upper bound (e.g. =, where and an arbitrary upper bound of ). Given I n = [ a n , b n ] {\displaystyle I_{n}=[a_{n},b_{n}]} for some n ∈ N {\displaystyle n\in \mathbb {N} } one can compute the midpoint m n := a n + b n 2 {\displaystyle m_{n}:={\frac {a_{n}+b_{n ...

  5. Imprecise probability - Wikipedia

    en.wikipedia.org/wiki/Imprecise_probability

    Walley defines upper and lower probabilities as special cases of upper and lower previsions and the gambling framework advanced by Bruno de Finetti. In simple terms, a decision maker's lower prevision is the highest price at which the decision maker is sure he or she would buy a gamble, and the upper prevision is the lowest price at which the ...

  6. Bhatia–Davis inequality - Wikipedia

    en.wikipedia.org/wiki/Bhatia–Davis_inequality

    Let m and M be the lower and upper bounds, respectively, for a set of real numbers a 1, ..., a n, with a particular probability distribution. Let μ be the expected value of this distribution. Then the Bhatia–Davis inequality states: ().

  7. Completeness (order theory) - Wikipedia

    en.wikipedia.org/wiki/Completeness_(order_theory)

    But this is just the least element of the whole poset, if it has one, since the empty subset of a poset P is conventionally considered to be both bounded from above and from below, with every element of P being both an upper and lower bound of the empty subset. Other common names for the least element are bottom and zero (0).

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