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A graph that shows the number of balls in and out of the vase for the first ten iterations of the problem. The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the paradoxical, or at least non-intuitive, nature of infinity.
The ping-pong lemma was a key tool used by Jacques Tits in his 1972 paper [2] containing the proof of a famous result now known as the Tits alternative. The result states that a finitely generated linear group is either virtually solvable or contains a free subgroup of rank two.
The definitions can be generalized to functions and even to sets of functions. Given a function f with domain D and a preordered set (K, ≤) as codomain, an element y of K is an upper bound of f if y ≥ f (x) for each x in D. The upper bound is called sharp if equality holds for at least one value of x. It indicates that the constraint is ...
A bounded operator: is not a bounded function in the sense of this page's definition (unless =), but has the weaker property of preserving boundedness; bounded sets are mapped to bounded sets (). This definition can be extended to any function f : X → Y {\displaystyle f:X\rightarrow Y} if X {\displaystyle X} and Y {\displaystyle Y} allow for ...
lowest points win Pickleball is a racket or paddle sport in which two players (singles) or four players (doubles) use a smooth-faced paddle to hit a perforated, hollow plastic ball over a 34-inch-high (0.86 m) net until one side is unable to return the ball or commits a rule infraction.
The terms out of bounds or out-of-bounds refers to an active participant or component of a game (e.g., player or ball ) being outside the playing boundaries of the field of a sport. The legality of going out of bounds (intentionally or not), and the ease of prevention, vary by sport.
Modern-day Spaldeen. A Spalding Hi-Bounce Ball, often called a Spaldeen or a Pensie Pinkie, is a rubber ball, described as a tennis ball core without the felt. [1] These balls are commonly used in street games developed in the mid-20th century, such as Chinese handball (a variation on American handball), Australian Handball, stoop ball, hit-the-penny (involving trying to make a penny flip on a ...
Ping-pong lemma, any of several mathematical statements for proving that some elements in a group acting on a set freely generate a free subgroup of that group; Ping-pong mechanism, a type of biochemical reaction characterized by its enzyme kinetics