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- How exactly does Knuths Up-Arrow notation work?
Just to get more of a feel for the arrow-notation and how rapidly the numbers can grow, let's extend the example one stage further in a couple of different ways First, what about $2↑↑↑4$? This is the same as $2↑↑ (2↑↑ (2↑↑2))$ which, using the working above, we know is $2↑↑65536$ In words, this is a tower of $65336$ twos! Second, what if we had four arrows? It turns out
- big numbers - How much bigger is 3↑↑↑↑3 compared to 3↑↑↑3 . . .
3↑↑↑3 is already mind-bogglingly large, but how much larger is 3↑↑↑↑3? Is it so large that it is simply around 3↑↑↑↑3 times larger than 3↑↑↑3? Or is there another way to express its magnitude in te
- What does this symbol ↑ mean? - Mathematics Stack Exchange
Sorry for my bad english I have a question about postfix expression , but i dont what symbol ↑ mean ? Thank for your help Find the value of the postfix expression: 2 2 4 + 3 2 ↑ + 5 3 + * –
- How does it work? - Mathematics Stack Exchange
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- 3↑↑↑3= ? but with 10 instead of 3 ( approximation, order of magnitude )
3↑↑↑3 being the first really huge number in the awesome crescendo of Graham's number, I suspect that it is still within the grasp of imagination, but it would help to get it in terms of 10 instead of 3
- Solving tricky Knuth Up Arrow Notations - Mathematics Stack Exchange
m↑↑-2 = log m (m↑↑-1) = log m 0 = -infinity (in other words, it is undefined) This seems to be the only logical extension of the double-arrow operator to nonpositive integer "exponents"
- Ordinal Arithmetic: Why is ε0 = ω^ω^ω^ω. . . - Mathematics Stack Exchange
In other words, in this notation, why not continue the pattern of ω+ω, ω*ω, ω^ω, ω↑↑ω, and so on, using ω↑↑ω instead of ε0? Is there any reason for ending that pattern with exponentiation, rather than using tetration and other super-operators?
- Is this number, N, greater than Graham’s Number?
@DaveL Renfro I intended to write k ↑ (googleplex amount of times) k Is this not the same as k ↑^k k Or am I not understanding the “to the power of” notation in terms of Knuth’s up-arrow notation?
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