Largest number?

Question

Who can define the largest number? Infinities and transfinities excluded! Also, no appending anyone else's answer with "+1" or the like.

Yes, I realize there is no 'largest number'. I just want to see how big you guys and gals can make your numbers.

Answer 1

The World Champion largest number, listed in the latest Guinness Book of Records, is an upper bound, derived by R. L. Graham, from a problem in a part of combinatorics called Ramsey theory.

Graham's number is much larger than other well known large numbers such as a googol and a googolplex, and even larger than Moser's number, another well-known large number.

Graham's number cannot be expressed using the conventional notation of powers, and powers of powers. If all the material in the universe were turned into pen and ink it would not be enough to write the number down. Consequently, this special notation, devised by Donald Knuth, is necessary.

3^3 means '3 cubed', as it often does in computer printouts.

3^^3 means 3^(3^3), or 3^27, which is already quite large: 3^27 = 7,625,597,484,987, but is still easily written, especially as a tower of 3 numbers: 3^3^3.

3^^^3 = 3^^(3^^3), however, is 3^^7,625,597,484,987 = 3^(7,625,597,484,987^7,625,597,484,987), which makes a tower of exponents 7,625,597,484,987 layers high.

3^^^^3 = 3^^^(3^^^3), of course. Even the tower of exponents is now unimaginably large in our usual notation, but Graham's number only starts here.

Consider the number 3^^^...^^^3 in which there are 3^^^^3 arrows. A largish number!

Next construct the number 3^^^...^^^3 where the number of arrows is the previous 3^^^...^^^3 number.

An incredible, ungraspable number! Yet we are only two steps away from the original ginormous 3^^^^3. Now continue this process, making the number of arrows in 3^^^...^^^3 equal to the number at the previous step, until you are 63 steps, yes, sixty-three, steps from 3^^^^3. That is Graham's number.

P.S. Or is it Graham's number plus 1? :-)

Answer 2

What's the largest number?
There is no largest number! Why? Well, 1,000,000,000 (1 billion) can't be the largest number because 1 billion + 1 is bigger - but that is true for any number you pick. You can choose any big number and I can make a bigger one just by adding 1 to it.
What's a googol?
A googol is a 1 with a hundred zeroes behind it. We can write a googol using exponents by saying a googol is 10^100.

The biggest named number that we know is googolplex, ten to the googol power, or (10)^(10^100). That's written as a one followed by googol zeroes.
How do we name large numbers?
There's some disagreement in the English language about how to name large numbers. There are two systems, the American and the English:

Scientific
American: Number Notation

Thousand 1,000 10^3
Million 1,000,000 10^6
Billion 1,000,000,000 10^9
Trillion 1,000,000,000,000 10^12
Quadrillion 1,000,000,000,000,000 10^15
Quintillion 1,000,000,000,000,000,000 10^18


English:

Thousand 1,000 10^3
Million 1,000,000 10^6
Thousand Million 1,000,000,000 10^9
Billion 1,000,000,000,000 10^12
Thousand Billion 1,000,000,000,000,000 10^15
Trillion 1,000,000,000,000,000,000 10^18

Answer 3

There is no such thing as a highest possible number. No matter what number you have, there is always a larger one. (For example, you could always add 1 to your number to get a larger number).
What you are intending to ask is "what is the largest number that anyone has ever decided to give a specific name to?" It is very important to understand that this is a completely different question from the one you asked, because it is a question about human culture not about mathematics.

The largest number that has a commonly-known specific name is a "googleplex", which is a 1 followed by a googol zeros, where a "googol" is (a 1 followed by 100 zeros).

Answer 4

That is an easy question to answer. This is because the answer is you. You define what the largest number is because in reality, the largest number is what you can possibly imagine, infinities and the like excluded. If you think a number is the largest number, then it is, else...knowing that the number you just imagined can be larger makes your number seem smaller.

We define our own reality. Physics and Quantum Physics are just our ways of collectively trying to understand the world we are in.

So, in short, your largest number is just that...your largest number. Take your largest number, add it with everyone elses, then multiply it by itself...wait, no. Set it to the power of itself and it's still the smallest number in the universe.

Answer 5

Quadraplex+2

Answer 6

The largest named number is googolplex, which is 10^10^100. That is 1 followed by a googol (10^100) zeros. Do not confuse with Google.com. They wanted a name that could be trademarked.

Answer 7

largest number=1/0

Answer 8

"Largest number" is a human definition of a term, so it really has no meaning. But, how about this, "the total number of all of the smallest indivisable particles in the universe". Should be close enough for government work.

Answer 9

a googal or something like that is a 1 with 100 0's following it=1 x 10^100

Answer 10

40