Editing Talk:2435: Geothmetic Meandian
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> Can any of you come up with a mathematical proof that repeated application of F on a set of (say) positive real numbers is guaranteed to converge toward a single real number | > Can any of you come up with a mathematical proof that repeated application of F on a set of (say) positive real numbers is guaranteed to converge toward a single real number | ||
− | Define: | + | Define: R(n) = range of F = max(An,Bn,Cn)-min(An,Bn,Cn), for iteration n<br> |
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− | R(n) = range of F = max(An,Bn,Cn)-min(An,Bn,Cn), for iteration n<br> | ||
We want to show that the range R(n) converges to 0.<br> | We want to show that the range R(n) converges to 0.<br> | ||
With the following notation: max(n) == max(An,Bn,Cn), ave(n)==ave(An,Bn,Cn), ..<br> | With the following notation: max(n) == max(An,Bn,Cn), ave(n)==ave(An,Bn,Cn), ..<br> |