Yes, a googolplex is smaller than Graham’s number.
For more information, read on
While the answer to this question is that a googolplex is smaller than Graham’s number, it’s important to note the vast difference in size between the two numbers. A googolplex is 10 to the power of googol (or 10 to the power of 100), which is already an incredibly large number with 101 digits. Graham’s number, on the other hand, is an unfathomably large number that is so big, it’s hard to even describe. Mathematician Ron Graham himself said, “I was at a conference recently where somebody told me that they had heard that I could describe Graham’s number. I said, ‘Well, go ahead and ask me.’ And they said, ‘Well, can you?’ I said, ‘No.'” However, mathematicians have attempted to describe it as the result of a complex mathematical equation involving hyper exponentiation.
To compare the two numbers, we can use a table:
| Number | Size |
|---|---|
| Googol | 10^100 |
| Googolplex | 10^(10^100) |
| Graham’s number | 3↑↑↑↑3 |
The notation used for Graham’s number (3↑↑↑↑3) refers to a series of exponential towers, where each level of the tower is raised to the power of the previous level. For example, 3↑3 is 3 to the power of 3, or 27. 3↑↑3 is 3 raised to the power of 3 raised to the power of 3, or 3^(3^3), which is a much larger number. This notation continues for Graham’s number, where each level of the tower is incredibly large.
While both numbers are indescribably large and difficult to comprehend, Graham’s number is exponentially larger than a googolplex. As mathematician Edward Kasner, who coined the term “googol,” said, “Typing a googolplex – which is 10^(10^100) – is impossible, since there are not enough particles in the known universe to put down in writing such a large number.” And yet, Graham’s number dwarfs even this mind-bogglingly large number.
Video response
In this YouTube video titled “What’s the Biggest Number That You Could Count To?”, the speaker discusses various aspects of counting large numbers. It is noted that someone who dedicates all their time to counting could potentially reach 1 million in 89 days. The natural limit of numerical expression is also discussed, suggesting that if the universe is filled with Planck volumes, it is impossible to contain more digits. The significance of Graham’s number is also explored, as it is the largest number that can be counted to produce an exact replica of a person. The speaker suggests that if the universe is bigger than a Googleplex, there could be other versions of people existing elsewhere in the same universe.
Check out the other answers I found
(This might sound familiar, as Google was named after this number, though they got the spelling wrong.) Graham’s number is also bigger than a googolplex, which Milton initially defined as a 1, followed by writing zeroes until you get tired, but is now commonly accepted to be 10googol=10(10100).
No, googolplex is not the biggest number ever. While googolplex is an incredibly large number, it is dwarfed by much larger numbers. In particular, it is possible to create numbers with many more digits. For instance, one of the largest numbers ever defined is Graham’s number, which has as many as 13,064 digits.
HAHAHAHAHAHAHAHA!!!
Not even close. Not even remotely close. Not even funny, how not even close these two numbers are. They aren’t in the same ballpark, the same world, the same universe, the same multi-universe.
Googolplexian is “ten to the power googolplex”, while googolplex is “ten to the power googol”, and googol is “ten to the power one hundred”. In other words, googol is 1 followed by a hundred zeroes, googolplex is 1 followed by a googol zeroes, and googolplexian is 1 followed by a googolplex of zeroes.
Large?
That’s nothing. Less than microscopic. Negligible. Peanuts, smashed to bits with a sledgehammer and then crushed in a particle accelerator. A single quark, compared with a googolplexian universes, is still far from representing just how tiny googolplexian is compared to Graham’s number.
Seriously, I’m not exaggerating.
Look:
[math]\displaystyle \text{googol} = 10^{100} %3C \left(3^3
ight)^{100} = 3^{300} %3C 3^{3^{3^3}} = 3\uparrow\!\uparrow 4[/math]The mighty goo…
Topic expansion
I’m sure you’ll be interested
What is bigger than Graham’s number?
The reply will be: Other specific integers (such as TREE(3)) known to be far larger than Graham’s number have since appeared in many serious mathematical proofs, for example in connection with Harvey Friedman’s various finite forms of Kruskal’s theorem.
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Is there any number bigger than a googolplex?
The response is: What’s bigger than a googolplex? Even though a googolplex is immense, Graham’s number and Skewes’ number are much larger. Named after mathematicians Ronald Graham and Stanley Skewes, both numbers are so large that they can’t be represented in the observable universe.
In respect to this, How many zeros are there in Graham’s number?
Answer to this: 100 zeros
It is a one followed by 100 zeros. (Fun fact: this number inspired the name of the search engine Google, but the company’s founders accidentally misspelled it when checking whether the web domain was still available. The rest is history.)
How many zeros are in a Googolplexian? Response to this: 10100 zeroes
Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes; that is, a 1 followed by a googol of zeroes.
Hereof, Is Graham’s number bigger than a googolplex? The response is: See YouTube or wikipedia for the defination of Graham’s number. A Googol is defined as 10 100. A Googolplex is defined as 10 Googol. A Googolplexian is defined as 10 Googolplex. Intuitively, it seems to me that Graham’s number is larger (maybe because of it’s complex definition).
One may also ask, What is a googolplex number? One such number is googolplex, which is 10 to the power of a googol, or 1 followed by a googol of zeros. The word googol was introduced in Mathematics and the Imagination, a book written by Edward Kasner and James R. Newman in 1940 to survey the field of mathematics for the layperson.
Also to know is, What is Graham’s number?
As an answer to this: Graham’s number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes’s number and Moser’s number, both of which are in turn much larger than a googolplex.
Similarly, How many books can a googolplex print? Response will be: It thus became standardized to 10 (10100) = 10 10100, due to the right-associativity of exponentiation. A typical book can be printed with 10 6 zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 10 94 such books to print all the zeros of a googolplex (that is, printing a googol zeros).
Then, Is Graham’s number bigger than a googolplex? See YouTube or wikipedia for the defination of Graham’s number. A Googol is defined as 10 100. A Googolplex is defined as 10 Googol. A Googolplexian is defined as 10 Googolplex. Intuitively, it seems to me that Graham’s number is larger (maybe because of it’s complex definition).
Also asked, What is a googolplex number? In reply to that: One such number is googolplex, which is 10 to the power of a googol, or 1 followed by a googol of zeros. The word googol was introduced in Mathematics and the Imagination, a book written by Edward Kasner and James R. Newman in 1940 to survey the field of mathematics for the layperson.
Moreover, How big is Graham’s number?
Response to this: Graham’s number is bigger the number of atoms in the observable Universe, which is thought to be between 10 78 and 10 82. It’s bigger than the 48th Mersenne prime , the biggest prime number we know, which has an impressive 17,425,170 digits.
Is googolplexian less than 3 6? So, Googolplexian is much smaller than a tower of exponents of 3 ‘s of length 6, or in other words Googolplexian is less than 3 ↑↑ 6. (using Knuth’s up-arrow notation .) Now, compare this with just the first layer of Graham’s number,i.e., 3 ↑↑↑↑ 3.