Mathematics Stack Exchange
Mathematics Stack Exchange

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
13
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1 answer

Graham's number expressed using xkcd's "Knuth Paper-Stack Notation"

The title text for xkcd #1162 describes a method for expressing extremely large numbers: Knuth Paper-Stack Notation: Write down the number on pages. Stack them. If the stack is too tall to fit in the room, write down the number of pages it would…
fintelia
  • 243
10
votes
3 answers

What is the biggest number ever used in a mathematical proof?

Probably a proof (if any exist) that calls upon Knuth's up-arrow notation or Busy Beaver.
Ami
  • 938
10
votes
5 answers

Is there a number so large that we could never calculate it?

Note that I edited this post significantly to make it more clear (as clear as I think I could possibly make it). First, let me mention what I am NOT asking: I am NOT asking for the largest number we could calculate. I am NOT asking if there is a…
user251299
8
votes
1 answer

If I call the Ackermann Function with Graham's number as both of its arguments will it be less than $g_{65}$

In xkcd comic 207 it states that [xkcd] means calling the Ackermann function with Graham's number as the arguments just to horrify mathematicians. $A(g_{64},g_{64})$ In this explanation it states that Even simply making $g_{65}$ dwarfs the…
user288447
  • 248
6
votes
5 answers

Is Rayo's number really that big?

I was reading about large numbers, and came across Rayo's Number which is defined to be the smallest integer that is not nameable by any expression in the language of set theory that contains less than $10^{100}$ symbols. Now, my question is: Is…
Andrei Kh
  • 2,569
5
votes
2 answers

Approximation of (n^n)^n

To be specific, what is the best way to calculate the first 10 digits decimal approximation of $$ \large \left(123456789^{123456789}\right)^{123456789}$$? Even WolframAlpha gives the result in a power of 10 representation as $$ \large…
neat
  • 51
5
votes
2 answers

When does Busy Beaver surpass TREE(3)?

I saw a question which asked, "When does Busy Beaver surpass TREE(n)?" I am asking a somewhat different question, about a specific value of TREE. I know that TREE(3) is an unimaginably vast number, far more than even Graham's number. I would be…
user107952
  • 20,508
5
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0 answers

First $n$ digits of Graham's Number

I know using Euler's Totient function, it's easy to find the last $n$ digits of Graham's number (or any large repeating power tower), but is there any known way to find the first $n$ digits of Graham's Number? How about in binary? Or in any base…
dspyz
  • 850
5
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1 answer

Can someone explain TREE(3) in extremely simple terms?

I have recently begun getting interested in the field of googology, or as your tags list it, "big numbers." One of the first things I saw mentioned was the famous TREE(3) function. I am at a high school math level, and most of it was…
CollinB
  • 151
4
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1 answer

Comparing big numbers.

Let $G_{64}$ is a Graham Number: https://googology.wikia.org/wiki/Graham%27s_number $TREE(3)$ is a particular value of a special sequence $TREE(k)$ https://googology.wikia.org/wiki/TREE_sequence $D^{5}(99)$ is a output of program…
mkultra
  • 1,382
3
votes
1 answer

Graham's Number on the Next Layer And TREE(3)

We all know how we calculate Graham's number. If you don't, a quick google search will familiarise you with the notation used and the G() function that is used. Now I learnt about Graham's number from Numberphile which is probably where that Google…
Mattia Marziali
  • 45
2
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1 answer

How do we know that Loader is bigger or grows faster than TREE or SSCG?

From what I have gathered online about these numbers, they say that Loader's Number is larger than TREE(3) or SSCG(3) or similar. The reasoning I have seen goes is that Loader's Number is the largest computable number and TREE(3) and SSCG(3) are…
CPlus
  • 183
2
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2 answers

How can I calculate or think about the large number 32768^1049088?

I decided to ask myself how many different images my laptop's screen could display. I came up with (number of colors)^(number of pixels) so assuming 32768 colors I'm trying to get my head around the number, but I have a feeling it's too big to…
Aaron Anodide
  • 623
1
vote
1 answer

Does this text based Tree Function stay finite?

Define $f(k)$ to be the maximal natural number $n$ such that there exist $n$ strings $s_1,\dots,s_n$ from the alphabet $\{1,2\}$ such that no letter is repeated more than $3$ times in a row, for all $1\leq i \leq n$, the string $s_i$ has length…
look at me
  • 29
1
vote
1 answer

Is the number of digits in Graham's number greater than the number of protons in universe (~10^122)?

I am wondering, is the number of digits in Graham's number greater than the number of protons in the known universe (~10^122)? Or is there some other 'big' lower bound to the number of digits in G64?
C Shreve
  • 561
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