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Questions tagged [big-numbers]

For questions relating to the computation, estimation and properties of extremely large finite quantities that are not usually used in mainstream mathematics. This is not for questions that just have large numbers; the fact that a number is very large has to affect the question.

For questions relating to the handling of large finite numbers. This is related to googology, which is the study and nomenclature of large numbers.

To place a scale, numbers around the size of a googol ($10^{100}$) and larger are considered "large".

270 questions
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In what sense would Graham's tree be virtually the same as TREE(3)?

How Big would "Graham's Tree" be? I'm coming off this post which asks about the size of the number which we would obtain by replacing the 3's in Graham's number construction by TREE(3). The first answer there mentions that it'd be pretty much the…
Ryder Rude
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A question about relation between two fast growing sequences.

Let $TREE(n)$ and $tree(n)$ are Kruskal' tree sequences. The second one is called weak. Prove that $TREE(3)>tree^{tree^{tree^{tree^{tree^{8}(7)}(7)}(7)}(7)}(7)$ You can see that inequality in every article about $TREE(3)$ and always it is left…
mkultra
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Very weak lower bound for TREE 3.

First of all i am not looking for very accurate lower bound. It would be enough to me the following : Prove that $TREE(3)>f_{\omega +2}(3)$ (here that function $f$ comes from fast growing hierarchy) Generally i don't know how to solve it. I have…
mkultra
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What is the smallest number $n$ , such that $n\uparrow^4 n>3\uparrow^5 3$ holds?

What is the smallest number $n$, such that $$n\uparrow^4 n>3\uparrow^5 3$$ holds ? $\uparrow$ stands for Knut's up-arrow-notation and is defined as follows $a\uparrow b=a^b$ $$a\uparrow \uparrow b=a\uparrow a\uparrow ...\uparrow a\uparrow a$$ with…
Peter
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Find the biggest number from given data below

Maths problem : $$(9^{62773} + 2)^{83721}$$ Now here is the rest of the problem. After finding the huge number I have to find its digital sum. If you don't know what that means just give me the answer to the problem. Please try to solve it also…
Murtuza Vadharia
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Does this "tree like" function stay finite?

Or more importantly, does it have a name? The function f(k)=x I have found goes under these rules, There is a group of n strings containing k characters Each string is 1 character longer than the last. Ex: 1, 22, 333... Every string cannot…
look at me
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Survival of TREE(3) under iterated logarithms

Instead of base 10 or base e, let the base of our logarithm be a positive integer B. Take log base B of TREE(3), B times, or stop if the answer is negative before B iterations. Say that TREE(3) does not "survive" if the answer is negative for B or…
Richard Peterson
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Where is $G64\uparrow \uparrow G64$ in the Fast-growing hierarchy?

I am trying to find out how $G64\uparrow \uparrow G64$ can be represented by the Fast-growing hierarchy, but I do not know how this can be done. Is there a way to simply convert between those two notations?
Abanob Ebrahim
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Theorems only valid for huge numbers

I am trying to find a theorem that is valid only for very large numbers. Example: There are numbers which have more than 100 distinct factors. Above theorem satisfies this condition, but it is a trivial one. What I would like is not a trivial one…
xycf7
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What is the value of X in (3,3(1)X,2) = (3,3(1)3,3)

I was reviewing Deedlit's awesome explanation for how the rules of planar arrays work at How can the number $\left\langle \matrix {3&3\\3&3}\right\rangle $ be described? as well as https://qntm.org/planar and https://mrob.com/users/chrisb/ in an…
Dave Rebus
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Ackerman numbers, arrow notation

How to compare $3^{3^{3^3}}$ and to $3\uparrow (3\uparrow \uparrow 3)$. (Ackerman number, arrow notation)? Are these two numbers equal?And also, how to compare $3\uparrow (3\uparrow \uparrow 3)$ with googol and googolplex? Thank you.
user60465
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How Big would "Graham's Tree" be?

What if in Graham’s Number every “3” was replaced by “tree(3)” instead? How big is this number? Greater than Rayo’s number? Greater than every current named number?
Goodwin Lu
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What is the Googol root of a Googolplex?

$\text{Googol}=10^{100}$ $\text{Googolplex}=10^{\text{Googol}}=10^{{10}^{100}}$ What is $\sqrt[\text{Googol}]{\text{Googolplex}}$? I know that's the same as $\sqrt[10^{100}]{10^{10^{100}}}$ but I still wanna know, what does this equal? (I made this…
DeJeL
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How can the number $\left\langle \matrix {3&3\\3&3}\right\rangle $ be described?

http://qntm.org/planar shows how Jonathan Bowers defines numbers using $2D$-arrays. I would like to get a feeling how big such numbers are. How can the number $$\left\langle \matrix {3&3\\3&3}\right\rangle $$ be described using numbers defined by…
Peter
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Comparing large exponents.

I have come up with a way to compare large exponents, for example: I can tell which number is bigger in $12345^{78901}$ or $21346^{78900}$ within a few seconds without using calculator. So I have 2 questions. 1)Is it something important?(I dont know…
Pranav K
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