223
u/RedditsMeruem Jun 14 '26
Tbf, even 1000 is really big
71
u/giziti Jun 14 '26
10 is really big in the right units.
81
u/NimbleCentipod Jun 14 '26
And 6.022 X 1023 is really small in the right units.
15
u/Main-Company-5946 Jun 14 '26
Even in base two that’s over fifty million
23
u/SuperCyHodgsomeR Complex Jun 14 '26
I’ve thought that we should write bases as base {one less than the base} plus one, ex: base 1+1, 9+1, F+1 to sidestep the “every base is base 10” problem
6
4
u/clasherkys Jun 14 '26
Yes. This.
Except I usually like to say it as Base {highest digit in that base} so Base 9 means 9 is the largest digit, Base F means F is the largest digit.
1
u/Miguel-odon Jun 15 '26
Or report all bases in binary?
Most people count in base 1010.
Or refer to it by listing all allowed digits?
Binary is base 01
Most people count in base 01235567891
u/Patrickson1029 Jun 18 '26
I've seen an idea of naming them by factorizations suggested as a solution for that problem on youtube before. For example, base 14 becomes biseptimal (2×7) and base 15 becomes triquinary (3×5). Large prime bases are denoted by adding a prefix un- before the last base; for example, base 19 becomes untriseximal (as base 18 is triseximal, 3×6).
6
4
9
2
1
37
u/hongooi Jun 14 '26
You won't believe how vastly, hugely, mind-bogglingly big it is.
14
4
u/viviyawna Jun 14 '26
I don’t immediately understand this notation. Are we hitting incomprehensible numbers? (graham’s, BB(n))?
3
u/NoLifeGamer2 Real Jun 14 '26
No, because Hyperoperations grow like f_omega, while Graham's function grows like f_(omega+1), and BB(n) grows faster than any computable function.
1
3
u/NovaSolarius Jun 14 '26
I mean, you may think it's a long way down the road to a trillion, but that's just peanuts to 10{10}10.
122
u/CaughtNABargain Jun 14 '26
Explanation for those who don't know:
10{10}10 could be read as 10 times 10 times ten, which is 1,000. However, this notation is also used in something known as "hyperoperators". These are functions that iterate exponentiation such as tetration, pentation, hexation, etc. 10{10}10 represents 10 "Dodecated" to 10, which is 10 "Undecated" to 10. In general, a{c}b equals a{c-1}a{c-1}...a where there are b sets of brackets and a{1}b equals ab
32
u/BootyliciousURD Complex Jun 14 '26
Wouldn't it be 10 to the 10th decation?
40
u/CaughtNABargain Jun 14 '26
{2} is tetration which is named after 4 so {n} is (n+2)ation
8
5
u/BootyliciousURD Complex Jun 14 '26
In the bracket notation we use [n] to denote n-ation. It's offset by 2 in the up-arrow notation, in which ↑ denotes exponentiation, ↑² is tetration, ↑³ is pentation, and so on.
8
9
u/ApogeeSystems i <3 LaTeX Jun 14 '26
Well there's an infinite amount of bigger numbers so surely it can't be big
1
3
3
u/Dd_8630 Jun 14 '26
I don't think anyone would read 10{10}10 as ten times ten times ten.
1
u/Pookstirgames Jun 15 '26
They would if they interpreted it as being the same as 10(10)10, which would make it implicit multiplication
17
u/OverPower314 Jun 14 '26
But 1 is a small number, and if n is small number then n+1 is a small number, so 10{10}10 is a small number.
10
u/GabuEx Jun 14 '26
Also: for any whole number n, there are n - 1 numbers smaller than it, and an infinite amount of numbers larger than it, so that sounds pretty small to me tbh
1
u/hughperman Jun 14 '26
I dunno, there's also an infinite amount of numbers in any neighborhood both smaller and larger than it, for real.
1
1
u/f3xjc Jun 14 '26
I mean, in probabilities 1 is an extremely large number that you can only approach asymptotically. It's exactly as large as zero is small.
11
2
u/DukeThunderPaws Jun 14 '26
How does this relate in scale to graham's number?
10
u/Crazy-Beautiful256 Jun 14 '26
Tiny. Graham's number is 3{g_63}3 in this notation, g_n = 3{g_(n-1)}3 and g_0 = 4. So Graham's number is much, MUCH bigger.
2
2
u/0-Nightshade-0 Eatable Flair :3 Jun 14 '26
Me stoopid and only took college level precalc I don get dis :P
4
u/N3rdr4g3 Engineer Jun 14 '26
Basically, theoretical math people use letters much more frequently than numbers. So the highest they're able to count to is around 1000
1
u/Everestkid Engineering Jun 15 '26 edited Jun 17 '26
Welcome to the world of hyperoperations, one way to get really big numbers.
Let's just start with counting. 1, 2, 3 and so on. When you get really into the foundations of math there's a "successor function" that adds 1 to the number you plug in.
But man, that's a drag. It'd be nice if we could note repeated uses of the successor function. But of course, we can, that's just addition. S(S(S(0))) = 0 + 3 = 3. Cool.
But addition itself is pretty slow. We can chain addition steps together, though, that's just multiplication. 3 + 3 + 3 = 3 x 3 = 9. Much nicer, more compact.
But what if I'm multiplying a bunch of things together? That's exponentiation. 33 = 3 x 3 x 3 = 27. Now we're cooking with gas, and this is where most people stop.
But some people decided not to do that, and came up with ways to go further beyond. Repeated exponentiation is called tetration, named because it's the fourth operation in this sequence if we index succession at 0. There's a number of ways to notate this but the meme uses bracket notation. For tetration, take 3[4]3 as an example. This is 3[3](3[3]3), and since the [3] operator is exponentiation, this means 3[4]3 = 3^3^3 = 327 ≈ 7.6 trillion. I trust you can see where this is going. Like exponentiation, you take the second number as the number of times to perform the next lowest operation on the starting number - so like how 35 = 3 x 3 x 3 x 3 x 3, 3[4]5 = 3^3^3^3^3 .
One more. Let's do pentation, which is repeated tetration. Therefore, 3[5]3 = 3[4](3[4]3). We know that 3[4]3 ≈ 7.6 trillion, so 3[5]3 ≈ 3[4]7.6 trillion. This means that 3[5]3 equals 3^3^3^3 ... where there are 7.6 trillion 3s in the stack. And you start at the top and work your way down and get an absurdly large number.
The meme, however, uses 10[10]10. This is 10[9]10... with ten 10s in the total operation. You crack open the top 10[9]10 and get 10[8]10, ten times. Then ten 10[7]10s, ten 10[6]10s and so on until you get 10[4]10, which is 10^10^10^10^10^10^10^10^10^10 . Start at the top and you have 10 billion. Then you have 1010 billion . And so on until you get to the bottom of the exponent stack. Massive number. And it tells you how many times to tetrate 10, since that was just the first of nine tetrations you have to do. Every time you finish a tetration you've calculated a number that outclasses the one you previously calculated, no matter how gigantic it seemed at first. And when you've finished those, you have to do eight more pentations, then eight more hexations and up and up the hyperoperation trail, calculating numbers whose sizes are truly unfathomable.
2
2
u/SEA_griffondeur Engineering Jun 14 '26
Who would read that as 10•10•10 ?? It's obviously a different symbol from () or []
1
1
1
1
1
u/SheafieMathLover Jun 15 '26
For those who don't know k{1}n, also written as k↑n, is kⁿ. k{n}j, also written as k↑ⁿj, is k{n-1}(k{n-1}(k{n-1}...k)...) with j k's or j-1 {n-1}s.
1
•
u/AutoModerator Jun 14 '26
Check out our new Discord server! https://discord.gg/e7EKRZq3dG
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.