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In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
In the problem of envy-free cake-cutting, there is a cake modeled as an interval, and agents with different value measures over the cake. The value measures are accessible only via queries of the form "evaluate a given piece of cake" or "mark a piece of cake with a given value".
This page was last edited on 12 March 2021, at 23:29 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...
In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...
The following is known about the dimension of a finite-dimensional division algebra A over a field K: dim A = 1 if K is algebraically closed, dim A = 1, 2, 4 or 8 if K is real closed, and; If K is neither algebraically nor real closed, then there are infinitely many dimensions in which there exist division algebras over K.
The monkey and the coconuts is the best known representative of a class of puzzle problems requiring integer solutions structured as recursive division or fractionating of some discretely divisible quantity, with or without remainders, and a final division into some number of equal parts, possibly with a remainder.
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The division should be unanimously fair – each person should receive a piece believed to be a fair share. The "cake" is only a metaphor; procedures for fair cake-cutting can be used to divide various kinds of resources, such as land estates, advertisement space or broadcast time.