If n(r-1)+1 objects are put into n boxes, then at least one of the boxes contains ror more of the object
Answers
Answer:
Pigeonhole Principle: If k is a positive integer and k + 1 objects are placed into k boxes, then at least one ... none of the k boxes has more than one object. Then ... Create a box for each element y in the codomain of f .
Answer: As it is, the Pigeonhole principle Theorem.
Step-by-step explanation: If n + 1 objects are put into n boxes, at least one box contains two or more objects.
The abstract formulation of the principle: Let X and Y be finite sets and let f:A\rightarrow B be a function.
If X has more elements than Y, then f is not one-to-one.
If X and Y have the same number of elements and f is onto, then f is one-to-one.
If X and Y have the same number of elements and f is one-to-one, then f is onto.
Pigeonhole principle is one of the simplest but most useful ideas in mathematics. We will see more applications than proof of this theorem.
As by the Pigeonhole theorem - If “A” is the average number of pigeons per hole, where A is not an integer then
At least one pigeonhole contains ceil[A] (the smallest integer greater than or equal to A) pigeons
The remaining pigeonholes contain at most floor[A] (the largest integer less than or equal to A) pigeons
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