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Possible Answers:
undefined.
Last seen on: Wall Street Journal Crossword – November 11 2022 – Shifty Schemers
Random information on the term “Less than”:
In probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences.
Suppose { X k : k = 0 , 1 , 2 , 3 , … } {\displaystyle \{X_{k}:k=0,1,2,3,\dots \}} is a martingale (or super-martingale) and
almost surely. Then for all positive integers N and all positive reals ϵ {\displaystyle \epsilon } ,
And symmetrically (when Xk is a sub-martingale):
If X is a martingale, using both inequalities above and applying the union bound allows one to obtain a two-sided bound:
The proof shares similar idea of the proof for the general form of Azuma’s inequality listed below. Actually, this can be viewed as a direct corollary of the general form of Azuma’s inequality.
Random information on the term “undefined”:
In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the propensity of assuming different values). The term can take on several different meanings depending on the context. For example:
In ancient times, geometers attempted to define every term. For example, Euclid defined a point as “that which has no part”. In modern times, mathematicians recognize that attempting to define every word inevitably leads to circular definitions, and therefore leave some terms (such as “point”) undefined (see primitive notion for more).
This more abstract approach allows for fruitful generalizations. In topology, a topological space may be defined as a set of points endowed with certain properties, but in the general setting, the nature of these “points” is left entirely undefined. Likewise, in category theory, a category consists of “objects” and “arrows”, which are again primitive, undefined terms. This allows such abstract mathematical theories to be applied to very diverse concrete situations.