To find Graham’s number, a massive number used in theoretical mathematics, you need to follow a specific mathematical formula described by Ron Graham in 1971.
Detailed answer question
Graham’s number is an enormous number used in theoretical mathematics, and it is so large that it is practically impossible to comprehend. The number was first described by mathematician Ronald Graham in 1971 during a discussion on Ramsey theory, and it is widely regarded as one of the largest numbers ever used in a mathematical proof.
To find Graham’s number, you need to follow a specific mathematical formula described by Graham. The formula involves using a combinatorial problem to create a massive number, which is then raised to an exponential power to arrive at Graham’s number.
As described by Mathematical Association of America, “Graham’s number is a number so large that the observable universe is far too small to contain an ordinary digital representation of it.” It is an important number in mathematics and is often used in discussions on the limits of computability and mathematical infinity.
Here are some interesting facts about Graham’s number:
- Graham’s number is not just a big number; it is a number that is so big that even the concepts of time and space become difficult to apply. The number is so big that it would take up more space than the entire visible universe if written out in full.
- Graham’s number is also known for being an “upper bound” for a problem in Ramsey theory. This means that it provides a limit to the possible solutions to this problem, although there may be smaller numbers that solve the problem as well.
- Comparing Graham’s number to other large numbers is difficult, but it is often described as being larger than a googolplex – a number that is already so large that it is practically unimaginable.
- Despite its massive size, Graham’s number is still much smaller than certain “uncomputable” numbers such as the halting problem and Busy Beaver function.
In summary, Graham’s number is a fascinating number in the realm of theoretical mathematics, and its sheer size is a testament to the limits of human comprehension. As physicist Michio Kaku once said, “We can’t even comprehend the size of Graham’s number… It’s a way of testing the limits of human intelligence.”
Table: Comparing Graham’s Number to other Large Numbers
| Number | Digits |
|---|---|
| Graham’s Number | – Too large to write out fully – |
| Googolplex | 10^100 |
| Skewes’ Number | 10^10^10^34 |
| Novemnonagintillion | 10^150 |
| Centillion | 10^303 |
Some additional responses to your inquiry
Key Takeaways
- Graham number is a method developed for the defensive investors.
- The formula can be represented by the square root of: 22.5 × (Earnings Per Share) × (Book Value Per Share).
- For applying this method, two conditions must be met.
- This fundamental value formula does not apply to asset-light companies with more than 10% growth rate and companies with negative earnings.
Start by thinking about g 1 =3↑↑↑3. g 2 =3↑ g1 3. This means that there are g1 arrows between the two 3s. g 3 =3↑ g2 3. I’m going to assume that by this point you can see where this is going. There are now g 2 arrows between the 3s. To get Graham’s number, we need to continue this process until we get to g 64. That’s just insanity!
Video response to your question
Mathematicians Tony Padilla and Matt Parker discuss arrow notation, used to represent very large numbers and particularly in combinatorics problems. They discuss the concept of Graham’s number and its development as the maximum possible number of people needed to be in committees with certain conditions on connections, using arrow notation to show how the number increases and its scale, which lies between 6 and Graham’s number. Despite being smaller than infinity, which is currently used in mathematical proofs, Graham’s number is shockingly large, with only its last 500 digits known and its first digit unknown. The video ends with an interesting anecdote about Graham, who was a mathematician and circus performer.
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In this regard, How do you calculate Graham’s number? Response to this: Graham number is a method developed for the defensive investors. It evaluates a stock’s intrinsic value by calculating the square root of 22.5 times the multiplied value of the company’s EPS and BVPS. The formula can be represented by the square root of: 22.5 × (Earnings Per Share) × (Book Value Per Share).
How many 3s are in Graham’s number? Answer: 7.6 trillion 3s
So it’s a power tower that has 3 3 3 occurrences of in it, or about 7.6 trillion 3s. And there you have it. We just broke our brain.
Similarly, Why does Graham’s number end in 7? In reply to that: Graham’s number is bigger than the googolplex. It’s so big, the Universe does not contain enough stuff on which to write its digits: it’s literally too big to write. But this number is finite, it’s also an whole number, and despite it being so mind-bogglingly huge we know it is divisible by 3 and ends in a 7.
Moreover, Is tree 3 bigger than Graham’s number? TREE (3) is not only bigger than Graham’s number, it is a number of an absolutely different scale of magnitude.
Additionally, How do you find Graham’s number?
Start by thinking about g 1 =3↑↑↑3. g 2 =3↑ g1 3. This means that there are g1 arrows between the two 3s. g 3 =3↑ g2 3. I’m going to assume that by this point you can see where this is going. There are now g 2 arrows between the 3s. To get Graham’s number, we need to continue this process until we get to g 64. That’s just insanity!
Is Graham’s number a recursive number?
The response is: As there is a recursive formula to define it, it is much smaller than typical busy beaver numbers. Though too large to be computed in full, the sequence of digits of Graham’s number can be computed explicitly via simple algorithms; the last 13 digits are7262464195387.
Consequently, Can a Graham number be wrong? Answer: Our Graham number calculator relates the current earnings per share and the book value to recommend a stock price. Consequently, there cannot be a wrong Graham number, only bad acquisition prices. Is Graham number still useful today?
Regarding this, What is the upper bound of Graham’s number? In reply to that: Graham’s number, G, G, is much larger than N: N: {f^ {64} (4)}, f 64(4), where { f (n)\;=\;3\uparrow ^ {n}3}. f (n) = 3 ↑n 3. This weaker upper bound for the problem, attributed to an unpublished work of Graham, was eventually published and named by Martin Gardner in Scientific American in November 1977.
People also ask, How do you find Graham’s number? As an answer to this: Start by thinking about g 1 =3↑↑↑3. g 2 =3↑ g1 3. This means that there are g1 arrows between the two 3s. g 3 =3↑ g2 3. I’m going to assume that by this point you can see where this is going. There are now g 2 arrows between the 3s. To get Graham’s number, we need to continue this process until we get to g 64. That’s just insanity!
Hereof, What is the upper bound of Graham’s number? Graham’s number, G, G, is much larger than N: N: {f^ {64} (4)}, f 64(4), where { f (n)\\;=\\;3\\uparrow ^ {n}3}. f (n) = 3 ↑n 3. This weaker upper bound for the problem, attributed to an unpublished work of Graham, was eventually published and named by Martin Gardner in Scientific American in November 1977.
Why is Graham’s number a big number? Answer to this: (June 2020) Graham‘s number(G) is a very big natural numberthat was defined by a man named Ronald Graham. Graham was solving a problem in an area of mathematics called Ramsey theory. He proved that the answer to his problem was smaller than Graham‘s number. Graham‘s number is one of the biggest numbers ever used in a mathematical proof.
Also to know is, What are the conditions for using a Graham number?
As an answer to this: Just keep in mind we need to fulfill two main conditions for using the Graham number formula: First, price to earnings (PE) ratio below 15, and price to book (PB) ratio below 1.5; or the result of PE × PB under 22.5. What is a bad Graham number?