Difference between revisions of "Ramsey Number"

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{{!}}'''m, n'''{{!}}{{!}}'''1'''{{!}}{{!}}'''2'''{{!}}{{!}}'''3'''{{!}}{{!}}'''4'''{{!}}{{!}}'''5'''{{!}}{{!}}'''6'''{{!}}{{!}}'''7'''{{!}}{{!}}'''8'''{{!}}{{!}}'''9'''{{!}}{{!}}'''10'''{{!}}
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{{!}}<math>i=2</math>{{!}}{{!}}<math>10^7(1-\frac{1}{10^7})=9999999</math>       
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{{!}}<math>i=3</math>{{!}}{{!}}<math>10^7(1-\frac{1}{10^7})^2=9999998.0000001</math>
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{{!}}<math>i=4</math>{{!}}{{!}}<math>10^7(1-\frac{1}{10^7})^3=9999997.00000029999999 \approx 9999997.0000003</math>
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{{!}}<math>i=5</math>{{!}}{{!}}<math>10^7(1-\frac{1}{10^7})^4=9999996.000000599999960000001 \approx 9999996.0000006</math> 
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{{!}}<math>i=...</math>{{!}}{{!}}<math>...</math>
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{{!}}align="center"{{!}}'''Image X'''<ref>Napier, 1616, p. 46</ref>{{!}}{{!}}<math>i=101</math>{{!}}{{!}}<math>10^7(1-\frac{1}{10^7})^{100} \approx 9999900.00049505</math>
 
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==Examples==
 
==Examples==

Revision as of 15:58, 21 July 2011

This is a Helper Page for:
Pigeonhole Principle

Work In Progress

Definition

Ramsey number R(m, n) is the solution to the party problems, which ask the minimum number of guests that must be invited so that at least m will know each other or at least n will not know each other.

A Summary of Known Ramsey Numbers

r,s 1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 1 1 1 1
m, n 1 2 3 4 5 6 7 8 9
i=2 10^7(1-\frac{1}{10^7})=9999999
i=3 10^7(1-\frac{1}{10^7})^2=9999998.0000001
i=4 10^7(1-\frac{1}{10^7})^3=9999997.00000029999999 \approx 9999997.0000003
i=5 10^7(1-\frac{1}{10^7})^4=9999996.000000599999960000001 \approx 9999996.0000006
i=... ...
Image X[1] i=101 10^7(1-\frac{1}{10^7})^{100} \approx 9999900.00049505

Examples

  1. Napier, 1616, p. 46