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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 ...
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 ...
Baseball is a drinking game in which players shoot a ping-pong ball across a table with the intent of landing the ball in one of several cups of beer on the other end, doing so in a way combining beer pong and flip cup. The game typically consists of two teams of even numbers, one on each side of a table, and four cups set up on each side.
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.
This glossary defines terms related to the sport of table tennis.. Alternation of ends After each game, players switch sides of the table. In the last possible game of a match, for example the seventh game in a best of seven matches, players change ends when the first player scores five points, regardless of whose turn it is to serve.