Comments for Lucky's Notes

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simply click the up coming webpage — Sat, 18 May 2013 10:35:16 +0000

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blogspot.de — Wed, 15 May 2013 19:56:34 +0000

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Comment on Notes on infinite tetration by Anonymous

Anonymous — Wed, 15 May 2013 14:13:30 +0000

Hi. Thanks for the reply. Yeah, I spotted that too, shortly after my post. It’s interesting how powers are not associative (i.e. x^(x^x) does not equal (x^x)^x), unlike all the other operators everyone is used to (multiplication, addition, etc). I’d incorrectly assumed that because there were no brackets in the original tetration equation, that it would, but I guess that shows the dangers of making assumptions. Still, a bit ambiguous to write the problem x^x^x^.. without brackets given associativity doesn’t hold. Anyway, thanks for your reply

Comment on Notes on infinite tetration by Anonymous

Anonymous — Wed, 15 May 2013 13:18:27 +0000

Because the tower of x’s by convention means the limit of the sequence u(0) = x, u(i+1) = x^u(i), which converges for x upto 1.44-ish. Your argument would apply to the alternative sequence u(0) = x, u(i+1) = u(i)^x, which does not converge for any x > 1.

I suggest you put x = sqrt(2) and calculate the first few terms of each of the two sequences – it will quickly become obvious.

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kumarmunnait.blogspot.co.uk — Fri, 10 May 2013 15:20:23 +0000

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