Describe the biggest number (10^10^10^10^1000)
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 Vytron
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Describe the biggest number (10^10^10^10^1000)
Yet another big number thread. This one only allows number that can be described in some way.
I.e. you know how the number looks like, so you can compare a number that was described with any other number that was described, and tell which one is bigger. If you can't tell if it's bigger or not, then it's an invalid number for the thread.
Examples:
10^100
^Can be described as a 1 followed by 100 zeroes, so it's fine for the thread.
Graham Number
^Even though you can describe how this number is constructed, you can't describe the number itself (only the last digits of the number are known, not how it starts.)
2^15456978
^That one can't be described, i.e.:
3^246811
11^354
Can you tell which ones are bigger without a calculator?
So they're invalid entries.
This thread can still be very big by using previously described numbers to build bigger ones, but here's a difference:
10^10^100
Description: A 1 with a string of 0s where the number of 0s is a 1 followed by 100 zeroes.
It's fine with a straightforward description.
2^2^2^2^2
Description: 2 to the power of 2, 4 times.
^Invalid, you aren't meant to say how to construct the number, but how the actual number looks like (so describe the resulting 200352930... and such number.)
5469876145
^Has implicit description (doesn't need a description because you can see the number in full.)
In other words, posting the result of 2^15456978, 3^246811, or 11^354, or describing Graham's number is fine, but not just directions of how to arrive to the number (e.g. a number must be imaginable, like a 1 with some number of 0s afterwards, but must not need to be calculated).
I'll start with:
1
I.e. you know how the number looks like, so you can compare a number that was described with any other number that was described, and tell which one is bigger. If you can't tell if it's bigger or not, then it's an invalid number for the thread.
Examples:
10^100
^Can be described as a 1 followed by 100 zeroes, so it's fine for the thread.
Graham Number
^Even though you can describe how this number is constructed, you can't describe the number itself (only the last digits of the number are known, not how it starts.)
2^15456978
^That one can't be described, i.e.:
3^246811
11^354
Can you tell which ones are bigger without a calculator?
So they're invalid entries.
This thread can still be very big by using previously described numbers to build bigger ones, but here's a difference:
10^10^100
Description: A 1 with a string of 0s where the number of 0s is a 1 followed by 100 zeroes.
It's fine with a straightforward description.
2^2^2^2^2
Description: 2 to the power of 2, 4 times.
^Invalid, you aren't meant to say how to construct the number, but how the actual number looks like (so describe the resulting 200352930... and such number.)
5469876145
^Has implicit description (doesn't need a description because you can see the number in full.)
In other words, posting the result of 2^15456978, 3^246811, or 11^354, or describing Graham's number is fine, but not just directions of how to arrive to the number (e.g. a number must be imaginable, like a 1 with some number of 0s afterwards, but must not need to be calculated).
I'll start with:
1
Last edited by Vytron on Sat Mar 21, 2015 2:15 pm UTC, edited 7 times in total.

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Re: Describe the biggest number
10,000
The number can be described as the number of dots shown below:
The number can be described as the number of dots shown below:
Re: Describe the biggest number
My number can be described as the number of dots shown in the previous post, with the following addition:
Code: Select all
.
 Vytron
 Posts: 429
 Joined: Mon Oct 19, 2009 10:11 am UTC
 Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P
Re: Describe the biggest number
20,000
My number can be described as the total dots if you put GoogologyMaster's picture from 2 posts ago in front of a mirror, and count them all.
My number can be described as the total dots if you put GoogologyMaster's picture from 2 posts ago in front of a mirror, and count them all.
 SirGabriel
 Posts: 42
 Joined: Wed Jul 16, 2014 11:54 pm UTC
Re: Describe the biggest number (20k)
28,092
My number can be described as the total number of words in the Johannine literature in the Greek New Testament.
This description doesn't meet the requirements, but since the number contains an implicit description, it doesn't really need to.
My number can be described as the total number of words in the Johannine literature in the Greek New Testament.
This description doesn't meet the requirements, but since the number contains an implicit description, it doesn't really need to.
Re: Describe the biggest number (20k)
100,000
This is a one, followed by two zeroes, followed by a comma, followed by three zeroes.
This is a one, followed by two zeroes, followed by a comma, followed by three zeroes.
The biggest number (63 quintillion googols in debt)
Re: Describe the biggest number (20k)
10,000,000,000
A one followed by a number of zeroes equal to one followed by a zero.
If I were to come up with some kind of, I dunno, notation for this, it would be 1(1(1))
A one followed by a number of zeroes equal to one followed by a zero.
If I were to come up with some kind of, I dunno, notation for this, it would be 1(1(1))
 SirGabriel
 Posts: 42
 Joined: Wed Jul 16, 2014 11:54 pm UTC
Re: Describe the biggest number (20k)
Okay, let's move beyond implicit descriptions.
Let f(x) equal the number formed by stringing together every counting number from 1 to x (for example, f(12) = 123456789101112).
My number is f(17). For comparison, this is just over a septillion.
Let f(x) equal the number formed by stringing together every counting number from 1 to x (for example, f(12) = 123456789101112).
My number is f(17). For comparison, this is just over a septillion.
Re: Describe the biggest number (20k)
Vytron wrote:
2^15456978
^That one can't be described, i.e.:
3^246811
11^354
Can you tell which ones are bigger without a calculator?
Um, yes? A quick Fermi estimate gives:
11^8 = 2*10^8(roughly) (214358881 if my mental arithmetic is correct)
So 11^24=10^25
and 11^354=10^368 (ish)
2^10=10^3 (ish)
2^15456978 = about 10^4700000
3^4=81; 3^6=729; 3^8=6569
ergo 3^17=10^8 (ish)
And 3^246811 = 10^130000 (ish)
They're thousands of orders of magnitude different!
So, uh, 2^15456978 is biggest.
Was this a trick question or something?
Anyway, my number is 31415926535897932384623433.
sorry I'll stop showing off now...
If it looks like a duck, and quacks like a duck, we have at least to consider the possibility that we have a small aquatic bird of the family Anatidae on our hands. –Douglas Adams
 SirGabriel
 Posts: 42
 Joined: Wed Jul 16, 2014 11:54 pm UTC
Re: Describe the biggest number (20k)
Using the same function as my previous post: f(100)
Re: Describe the biggest number (20k)
Borrowing SirGabriel's function: f(f(3))
Re: Describe the biggest number (20k)
Those calculations weren't QUICK though, were they?
g (x) is a function that strings together f(1), f(2), and so on until f(x). So, g(3) = 112123.
My number is g(26), which is a, bit more than 330 digits long. The previous was around 250, I think.
g (x) is a function that strings together f(1), f(2), and so on until f(x). So, g(3) = 112123.
My number is g(26), which is a, bit more than 330 digits long. The previous was around 250, I think.
 SirGabriel
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 Joined: Wed Jul 16, 2014 11:54 pm UTC
Re: Describe the biggest number (20k)
Reecer6 wrote:Those calculations weren't QUICK though, were they?
g (x) is a function that strings together f(1), f(2), and so on until f(x). So, g(3) = 112123.
My number is g(20), which is a, bit more than 200 digits long.
A bit more than 200 digits isn't enough. f(f(3)) = f(123) > 10^260
Edit: Reecer6 edited his post while I was in the process of replying to it.
 SirGabriel
 Posts: 42
 Joined: Wed Jul 16, 2014 11:54 pm UTC
Re: Describe the biggest number (20k)
h(x) is a function that strings together g(1), g(2), and so on until g(x). So h(3) = 1112112123
i(x) is a function that strings together h(1), h(2), and so on until h(x). So i(3) = 111121112112123
My number is i(9), which, if I'm not mistaken, has nearly 500 digits.
i(x) is a function that strings together h(1), h(2), and so on until h(x). So i(3) = 111121112112123
My number is i(9), which, if I'm not mistaken, has nearly 500 digits.
Re: Describe the biggest number (20k)
10^500
This is a one followed by 500 zeroes with commas interspersed accordingly.
This is a one followed by 500 zeroes with commas interspersed accordingly.
The biggest number (63 quintillion googols in debt)
 SirGabriel
 Posts: 42
 Joined: Wed Jul 16, 2014 11:54 pm UTC
Re: Describe the biggest number (20k)
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
This is the number 9 repeated 1000 times.
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
This is the number 9 repeated 1000 times.
Re: Describe the biggest number (20k)
i(20) has over ni... just under ten thousand digits, so I'll put that as my number. Why the big difference? So it's clear enough that it's bigger than a 9 repeated a thousand times.
You know what? I can just post this. This is i(11).
And this is the previous number.
Mine is clearly bigger than it!
To describe these numbers without using an indecipherable function...
Start wrting 1s. Keep putting down 1s until you get four. The four is for the number of iterations the function's gone through, so you can repeat this at higher levels. Once you have four, put down the next higher number  a 2. Now, start this over again but with three 1s. After the third 1, put a 2 again. Keep going like this, reducing numbers of 1s, until you have written four 2s. Now, put down a 3. The pattern repeats as it did with the 2, starting with three 1s. Stop doing this once you get to the number you plugged into the function. Here, it's 11.
Re: Describe the biggest number (20k)
My number is a 1 followed by the same number of 0s as there are dots in this picture:
 SirGabriel
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Re: Describe the biggest number (20k)
10^(10^10)
A one followed by ten billion zeroes.
A one followed by ten billion zeroes.

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Re: Describe the biggest number (20k)
10^10^20
one followed by 100,000,000,000,000,000,000 zeros
one followed by 100,000,000,000,000,000,000 zeros
 Vytron
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 Joined: Mon Oct 19, 2009 10:11 am UTC
 Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P
Re: Describe the biggest number (20k)
@patzer: Okay, you're describing how to compare such numbers without a calculator, so you could send numbers like 2^15456978 as long as you describe how they're bigger like that (this applies to everyone.)
I send:
2x10^10^20
In scientific notation, this is a 2 followed by 100,000,000,000,000,000,000 zeros.
I send:
2x10^10^20
In scientific notation, this is a 2 followed by 100,000,000,000,000,000,000 zeros.

 Posts: 5
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Re: Describe the biggest number (2x10^10^20)
10^(10^20+1)
1 followed by 100,000,000,000,000,000,001 zeros, five times larger than the previous entry
1 followed by 100,000,000,000,000,000,001 zeros, five times larger than the previous entry
 Vytron
 Posts: 429
 Joined: Mon Oct 19, 2009 10:11 am UTC
 Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P
Re: Describe the biggest number (2x10^10^20)
6x10^(10^20+1)
In scientific notation, a 6 followed by 100,000,000,000,000,000,001 zeros.
Yes, count them, this is:
6
SIX
Times larger than the previous entry. Like, whoa, man!
In scientific notation, a 6 followed by 100,000,000,000,000,000,001 zeros.
Yes, count them, this is:
6
SIX
Times larger than the previous entry. Like, whoa, man!
Re: Describe the biggest number (2x10^10^20)
My number is 1 followed by 13 zeroes, which is then followed by the number one digit smaller than it, and then the number smaller than that, and so on. So, the first 40 digits of my number are 1000000000000099999999999999999999999998. My number is, more or less, repeating 13 digits 10,000,000,000,000 times. Well, it'll be less than that, since it'll get smaller towards the end, but that will only affect the last tenth, so it isn't too important.
 Vytron
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Re: Describe the biggest number (2x10^10^20)
Sorry, I don't think that's valid, if you can't count how many digits it has it's an "unimaginable number."
For instance, I have no idea if a number that repeated 13 digits 10,000,000,000,001 times would be bigger or smaller, or exactly how many times surpass it.
(the number you're sending is valid, but not its description)
It's important that the number you send is not "fuzzy", but that it's some concrete amount.
For instance, I have no idea if a number that repeated 13 digits 10,000,000,000,001 times would be bigger or smaller, or exactly how many times surpass it.
(the number you're sending is valid, but not its description)
It's important that the number you send is not "fuzzy", but that it's some concrete amount.
 Vytron
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Re: Describe the biggest number (2x10^10^20)
(Or you could, you know, send a number that repeats 13 digits 10,000,000,000,000 times, where those digits are 9999999999999, and it would be fine)
 SirGabriel
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Re: Describe the biggest number (2x10^10^20)
10^(10^100)
1 googolplex: a 1 followed by a googol of zeroes, where a googol is a 1 followed by 100 zeroes.
1 googolplex: a 1 followed by a googol of zeroes, where a googol is a 1 followed by 100 zeroes.
 Vytron
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Re: Describe the biggest number (2x10^10^20)
7x10^(10^100)
7 Googolplexes: A 7 followed by a googol of zeroes, where a googol is a 1 followed by 100 zeroes.
This is 7 times larger than the previous entry.
7 Googolplexes: A 7 followed by a googol of zeroes, where a googol is a 1 followed by 100 zeroes.
This is 7 times larger than the previous entry.

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Re: Describe the biggest number (2x10^10^20)
10^10^101
Googolplex^10, which is a one followed by as many zeros as a one followed by 101 zeros.
Googolplex^10, which is a one followed by as many zeros as a one followed by 101 zeros.
 SirGabriel
 Posts: 42
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Re: Describe the biggest number (2x10^10^20)
f(10^100)
The number of digits in this number can be described as two nines followed by ninetyseven eights followed by two nines followed by a zero.
The number of digits in this number can be described as two nines followed by ninetyseven eights followed by two nines followed by a zero.
 Vytron
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Re: Describe the biggest number (2x10^10^20)
I think GoogologyMaster's number is higher.
 SirGabriel
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Re: Describe the biggest number (10^10^101)
f(10^100) > 10^(9.98*10^101) > 10^10^101
 Vytron
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Re: Describe the biggest number (10^10^101)
But in your description you say:
"The number of digits in this number can be described as two nines followed by ninetyseven eights followed by two nines followed by a zero."
The number of digits that you describe are:
2 (the two nines)
+
97 (the 8s)
+
2 (the other two nines)
+
1 (the zero)
For a total of 102 digits.
While the description of GoogologyMaster's number:
"a one followed by as many zeros as a one followed by 101 zeros."
Means it has more than 102 digits (it has 1000... digits where those 0s are 101.)
"The number of digits in this number can be described as two nines followed by ninetyseven eights followed by two nines followed by a zero."
The number of digits that you describe are:
2 (the two nines)
+
97 (the 8s)
+
2 (the other two nines)
+
1 (the zero)
For a total of 102 digits.
While the description of GoogologyMaster's number:
"a one followed by as many zeros as a one followed by 101 zeros."
Means it has more than 102 digits (it has 1000... digits where those 0s are 101.)
Last edited by Vytron on Thu Mar 05, 2015 2:18 pm UTC, edited 1 time in total.

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Re: Describe the biggest number (10^10^101)
Vytron wrote:But in your description you say:
2 (the two nines)
+
97 (the 8s)
+
2 (the other two nines)
+
1 (the zero)
For a total of 100 digits.
This should be 102 digits (2+97+2+1=102)
Edit: It got corrected.
Anyway, I enter the number
10^10^200  1
The number of digits in this number is a one followed by 200 zeros, all digits are 9s.
Last edited by GoogologyMaster on Thu Mar 05, 2015 2:19 pm UTC, edited 1 time in total.
 Vytron
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 Joined: Mon Oct 19, 2009 10:11 am UTC
 Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P
Re: Describe the biggest number (10^10^101)
Edited right after you quoted.
 SirGabriel
 Posts: 42
 Joined: Wed Jul 16, 2014 11:54 pm UTC
Re: Describe the biggest number (10^10^101)
I did not say that my number has 102 digits, I said it has 998888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888990 digits.
The number of digits in the number of digits of my number is 102, just as with GoogologyMaster's number.
My new number is 10^10^200  1/(10^10^200)
The number of digits before the decimal and the number of digits after the decimal in this number are both a one followed by 200 zeroes, all digits are nines.
The number of digits in the number of digits of my number is 102, just as with GoogologyMaster's number.
My new number is 10^10^200  1/(10^10^200)
The number of digits before the decimal and the number of digits after the decimal in this number are both a one followed by 200 zeroes, all digits are nines.

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Re: Describe the biggest number (10^10^101)
Now I have a great idea. Suppose we had a sequence with some number of 0's and then zoom out so we can see more 0's. In this sequence, I zoomed out by 2x to see 4x as many zeros.
My number is 10^4^1000 which is Level 1000 in this sequence. (imagine zooming out 1000 powers of two)
My number is 10^4^1000 which is Level 1000 in this sequence. (imagine zooming out 1000 powers of two)
 SirGabriel
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 Joined: Wed Jul 16, 2014 11:54 pm UTC
Re: Describe the biggest number (10^10^101)
GoogologyMaster wrote:My number is 10^4^1000 which is Level 1000 in this sequence. (imagine zooming out 1000 powers of two)
I don't know about you, but I can't quickly estimate 4^1000 in my head.

 Posts: 5
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Re: Describe the biggest number (10^10^101)
4^1000 = 4^(2*500) = 16^500
So this number is bigger than 10^10^500.
So this number is bigger than 10^10^500.
Re: Describe the biggest number (10^10^101)
10^10^10^10
A discrete 10hyperhyperhypercube.
A discrete 10hyperhyperhypercube.
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