I went with the googoplex because i had a maths encyclopedia for kids that mentioned it It was like kriptonyte... until the other kid would say a googolplex and 1🤣
Why did they show an 8 every time he said "_th" power" (ex: he said 80th but the graphic showed 88. He said 40th but the graphic showed 48. He said 120th but the graphic showed 128). By the way, what he said was correct (the Shannon Number is 10^120, not 10^128) the graphics were wrong.
Probbly the editor is not a native speaker and misunderstood the 120th for 120 eigth, this trend to put 8's at the ordinal numbers is seen all throughout the video
At 11:26 the approximation for the lower bound of TREE(3) "written like this" does not make sense. I'm assuming the large digit 1 is meant to be an up-arrow. In which case it makes sense. It means we should continue the process of generating more 'g' numbers beyond 'g subscript 64' until we reach 'g subscript n' where n = 3 (187196 up-arrows) 3.
Not that it matters in practice but no chess position has even nearly 1000 moves. It is possible to construct positions with slightly more than 100 legal moves without promoted pieces, and perhaps 200 or so moves allowing for promotion (e.g., positions where a many pawns were promoted to a queen or another piece). But such positions are highly artificial. The average number of legal moves per side in most positions is probably closer to 30-40 at most. That still makes (40)^40 or about 10^64... which is about 1000 times larger than the number of Planck times that passed since the big bang.
Each move consists of 2 plies. If you just have 32 legal moves per ply, that's 1,024 possibilities per move. If you dislike this naming convention and think it's confusing... yeah.
No, Rayo's number is way bigger than TREE(4), because you can "encode" the way TREE works in first order set theory language. There are probably estimations out there of howany symbols are necessary, but for sure you should be able to do it with a few tens of thousands of symbols, and then it's pretty straightforward to iterate it as you please, so TREE will never be able to catch up. For very small values (typically 3), TREE is bigger because it takes a lot of symbols to get small numbers in FOST, but Rayo grows faster after a certain point.
e is, like most numbers, transcendental, meaning you would need to write down its digits forever to approximate it adequately, you want to do that? Go ahead, would probably be a more valuable use of your time than commenting on UA-cam videos.
7:08, your on-screen notation of arrow notation is flawed. At 7:08 you show a^n and then later you show a^n^n but you should show a^a and a^a^a and indicate that the tower of a’s is n high.
Grahamsnumber is a theory and cant exist in the real world due to its absurd proportion and will forever be immemorialized as a breakthrough phenomenon in mathematics
I have always preferred Asimov's definition of googol. Ten to the ten to the tenth. Ten to the ten billionth power. Much more elegant. And googolplex as ten to the googol power. Ten to the 100'th power seems arbitrary by comparison.
I have a great book called The Biggest Number in the World: A Journey to the Edge of Mathematics. If you're really interested in the subject of very large numbers, I can highly recommend it.
3:57 Prime counting function uses a natural log, never written as 'lg'. We've written that as log historically, log-sub-e, or since the late 1800s, ln as become more pervasive. One wonders where this notation came form.
Firstly, no, the prime-counting function does not "use" the natural logarithm. Its definition does not reference logarithms anywhere. Secondly, I assume you meant to say that the logarithm shown here should be the natural logarithm, but this is not even true. I traced the image back to Wolfram MathWorld, which states that this expression defines a function called the Riemann prime-counting function, where lg denotes the binary (base-2) logarithm. This is indeed an accepted abbreviation for the function. I don't like it because per the ISO standard, lg should denote the base-10 logarithm and lb the binary logarithm, but it is out there nonetheless. If you're wondering why the "ln" notation came about, it was probably to avoid confusion with the base-10 logarithm.
Eddington's is clearly not fixed, but as telescopes reach diminishing returns and we can see closer and closer to the Recombination event we should get some sort of upper bound.
7:26 it was shown very shortly, but I still noticed the statement "3^3^3 *= 3* = 3^27 = 7 625 597 484 987". 🤦😛 But that can be proven true when accepting (10^3)^48 = 10^(3*48) = 10^128. 🤣
Tbh googol was the first large number I used to flex when I was a kid 💀
I also used to googo-plex
Me too,I also flex Big Daddy Rayo's
I went with the googoplex because i had a maths encyclopedia for kids that mentioned it
It was like kriptonyte... until the other kid would say a googolplex and 1🤣
@@MarvnJoseph-oe6vxyeah, well you watch numberphile i bet
Why did they show an 8 every time he said "_th" power" (ex: he said 80th but the graphic showed 88. He said 40th but the graphic showed 48. He said 120th but the graphic showed 128). By the way, what he said was correct (the Shannon Number is 10^120, not 10^128) the graphics were wrong.
(10³)⁴⁸ = 10¹²⁸
WHAT??
(x^a)^b = x^a*b therefore (10^3)^48 = 10^3*48 = 10*144
I want to make the same comment it's 10¹⁴⁸
The actual verbally expressed numbers are correct, however.
He said (10³)⁴⁰ = 10¹²⁰ which checks out, and goes with the rest of the story
Probbly the editor is not a native speaker and misunderstood the 120th for 120 eigth, this trend to put 8's at the ordinal numbers is seen all throughout the video
Sirotta a 9 year old learns about raising a number by power.
Sirotta: "Well, 10^100"
Mathematicians: 🤯
6:20, *2.718… Although the narration does say the correct value, the screen shows 2.718. It also does so with equality is also incorrect.
You keep putting on number on screen, but saying another. Pick a lane.
It’s so annoying
This dude has the same relationship to the word “eighth” that the evil planetarium guy from South Park had with the letter “T.”
1:55: 3*48 = 128?
Yep trust me bro 😂
First and second number are different pronounced or on screen.
At 11:26 the approximation for the lower bound of TREE(3) "written like this" does not make sense. I'm assuming the large digit 1 is meant to be an up-arrow. In which case it makes sense. It means we should continue the process of generating more 'g' numbers beyond 'g subscript 64' until we reach 'g subscript n' where n = 3 (187196 up-arrows) 3.
Not that it matters in practice but no chess position has even nearly 1000 moves. It is possible to construct positions with slightly more than 100 legal moves without promoted pieces, and perhaps 200 or so moves allowing for promotion (e.g., positions where a many pawns were promoted to a queen or another piece). But such positions are highly artificial. The average number of legal moves per side in most positions is probably closer to 30-40 at most. That still makes (40)^40 or about 10^64... which is about 1000 times larger than the number of Planck times that passed since the big bang.
Each move consists of 2 plies. If you just have 32 legal moves per ply, that's 1,024 possibilities per move.
If you dislike this naming convention and think it's confusing... yeah.
If you think Tree(3) is big, it's insignificant compared to Tree(4).
I really enjoy your channel! Looking forward to new episodes!
There is the Busy Beaver between TREE and Rayo.
Is TREE(4) bigger than Rayo?
No, Rayo's number is way bigger than TREE(4), because you can "encode" the way TREE works in first order set theory language. There are probably estimations out there of howany symbols are necessary, but for sure you should be able to do it with a few tens of thousands of symbols, and then it's pretty straightforward to iterate it as you please, so TREE will never be able to catch up.
For very small values (typically 3), TREE is bigger because it takes a lot of symbols to get small numbers in FOST, but Rayo grows faster after a certain point.
Youre a real one for this
Nicely explained in record time - thanks! :)
6:19 euler's number is not 2.178 🤦
it's an approximation
e is, like most numbers, transcendental, meaning you would need to write down its digits forever to approximate it adequately, you want to do that? Go ahead, would probably be a more valuable use of your time than commenting on UA-cam videos.
Guys he meant that the 7 and the 1 are inverted, e is actually around 2.718
7:08, your on-screen notation of arrow notation is flawed. At 7:08 you show a^n and then later you show a^n^n but you should show a^a and a^a^a and indicate that the tower of a’s is n high.
Grahamsnumber is a theory and cant exist in the real world due to its absurd proportion and will forever be immemorialized as a breakthrough phenomenon in mathematics
Starting at 10:57, you say nodes several times when you mean colors.
No, the narration is correct. It's the visual that's wrong.
I have always preferred Asimov's definition of googol. Ten to the ten to the tenth. Ten to the ten billionth power. Much more elegant. And googolplex as ten to the googol power. Ten to the 100'th power seems arbitrary by comparison.
Avery informative educational video
I have a great book called The Biggest Number in the World: A Journey to the Edge of Mathematics.
If you're really interested in the subject of very large numbers, I can highly recommend it.
g TREE(Rayo’s Number) I think I win
3:57 Prime counting function uses a natural log, never written as 'lg'. We've written that as log historically, log-sub-e, or since the late 1800s, ln as become more pervasive. One wonders where this notation came form.
Firstly, no, the prime-counting function does not "use" the natural logarithm. Its definition does not reference logarithms anywhere.
Secondly, I assume you meant to say that the logarithm shown here should be the natural logarithm, but this is not even true. I traced the image back to Wolfram MathWorld, which states that this expression defines a function called the Riemann prime-counting function, where lg denotes the binary (base-2) logarithm. This is indeed an accepted abbreviation for the function. I don't like it because per the ISO standard, lg should denote the base-10 logarithm and lb the binary logarithm, but it is out there nonetheless.
If you're wondering why the "ln" notation came about, it was probably to avoid confusion with the base-10 logarithm.
What about the Busy Beaver sequence? Doesn't it bust them all?
It has been proven that Rayo(7339) is larger than Busy beaver of a googol
Busy beaver is smalller than Rayos number but it is bigger than all the other numbers
Well, all except Rayos number
6:36 this number in another name is: *ahem*
one nanehendiduetriacontitirahectedakillion (i think)
My body count
All men
Rayo's number is just goofy imo. It's not a fixed number in the same way that all the others are.
it is fixed, but it might as well be impossible to find
Eddington's is clearly not fixed, but as telescopes reach diminishing returns and we can see closer and closer to the Recombination event we should get some sort of upper bound.
Wait for big foot and biggedon
straight to the point... no time wasting ........ underrated
7:26 it was shown very shortly, but I still noticed the statement "3^3^3 *= 3* = 3^27 = 7 625 597 484 987". 🤦😛
But that can be proven true when accepting (10^3)^48 = 10^(3*48) = 10^128. 🤣
What is (10³)¹⁰⁰?
Fix the numbers dude
Why go to effort of showing the number but not saying it?!!! These are possibly the most unclear explanations of anything anywhere ever.
Nice try to ragebait
Maybe don't use a sexual monster's image in your videos?
Rayo cheated. U cant just say “my lowest number is greater than the highest number you can think off”. Rayo’s # > sixtynine(69)