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- What does this symbol ↑ mean? - Mathematics Stack Exchange
So "3 2 ↑" is probably supposed to mean "three to the power of two", or 3² With more context, one could be more sure (and probably write this as the most likely answer) $\endgroup$ – Marco13
- How exactly does Knuths Up-Arrow notation work?
We have that $2↑↑2 = 2^2 = 4$, so we need to calculate $2↑↑4$ This is a tower of four twos: $2^{2^{2^2}} = 2^{2^4} = 2^{16} = 65536$ 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
- 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
- 3↑↑↑3= ? but with 10 instead of 3 ( approximation, order of magnitude )
3↑↑↑3= (or near) in power tower of 10 or in ( Knuth ) arrow ↑ notation of 10 to get a sense of it's order of magnitude; I grasp numbers more easily with 10 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
- How does it work? - Mathematics Stack Exchange
When going through with learning Grahams number, I got stuck at $$3↑↑↑3$$ Working it through, we have $$3↑3=3^3$$ $$3↑↑3=3^{3^3}=3↑(3↑3)$$ As such, it would appear to me that $$3↑↑↑3=3^{3^{3^
- Is this number, N, greater than Graham’s Number?
$\begingroup$ @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? $\endgroup$ –
- Is 2 (6)3 (2↑↑↑↑3) equal to 2^65536? And if yes, is 2 (n)3 equal to 2 . . .
I am writing a paper for the last digits in a chain power of 2 I was wondering if 2↑↑↑↑3 is 2^65536 Beacouse 2↑↑↑3 is 65536 or 2^16 and is written as 2^2^ 2^2 16 times and 2↑↑3 is 16 or 2^4 and
- elementary set theory - ↑ and ↓ relations on measures (Durett . . .
In Rick Durrett's fourth edition of "Probability: Theory and Examples", an ↑ relation is defined on Theorem 1 1 1's sections (iii) and (iv): As stated, $\uparrow$ and $\downarrow$ are defined as:
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