What's the largest number in the world?

While there obviously isn't a largest number, the largest number which has ever meaningfully been thought of is pretty neat. If nothing else, the idea of Graham's number as an upper bound is hilarious to anyone who wants to think in purely physical terms.
 
The Grave said:
You never get it!

But if you do... then what's the smallest?

:seteacher:
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e^(10^120)) is the largest in our universe. Its inverse is the smallest.

No, I'm not entirely serious - but there may actually be some truth to that. (Scott Aaronson would probably know what I'm talking about.)
 
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well if by "smallest" you mean magnitude or you don't include negatives then the smallest is zero. The largest? There is no largest. Sorry. Infinity is not a number.
 
The googol number is pretty large, 10^100. But not as large as the googolplex, 10^10^100.

For the anecdote:
The name Google has been derived from the word "Googol" and has been spelled wrong by the founders Larry Page and Sergey Brin, as published in the book The Google Story by David A.
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I only have a finite set of numbers
(I use your human terms only to aid communication)

Zero < One < Many < All < Infinite

so you can see my order of precedence, if you mean by smallest Smallest non zero number then it will be One/All
 
The largest number? Twelve.
Everything above that is just made up from smaller numbers.

I am almost serious: A dozen is the largest number I can think of - without searching - that has a name and is not defined by using smaller numbers. A pair would be 2, but a gross is already defined as 12*12, the same holding true for other, much larger numbers, like the googol or googolplex. (I am not sure if I can define away astronomical constants. Possibly by observing that they are specific values rather than arbitrary numbers?)
 
Rasmus said:
The largest number? Twelve.
Everything above that is just made up from smaller numbers.

I am almost serious: A dozen is the largest number I can think of - without searching - that has a name and is not defined by using smaller numbers. A pair would be 2, but a gross is already defined as 12*12, the same holding true for other, much larger numbers, like the googol or googolplex. (I am not sure if I can define away astronomical constants. Possibly by observing that they are specific values rather than arbitrary numbers?)
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A score?
 
Rasmus said:
The largest number? Twelve.
Everything above that is just made up from smaller numbers.

I am almost serious: A dozen is the largest number I can think of - without searching - that has a name and is not defined by using smaller numbers. A pair would be 2, but a gross is already defined as 12*12, the same holding true for other, much larger numbers, like the googol or googolplex. (I am not sure if I can define away astronomical constants. Possibly by observing that they are specific values rather than arbitrary numbers?)
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I don't understand the reasoning here; I could use the word frumpty to denote the number 100, and say it isn't defined in terms of other numbers. But why not use the word hundred, which is a perfectly suitable word for exactly that number. Why is a dozen special opposed to, say, a million?
 
H'ethetheth said:
I don't understand the reasoning here; I could use the word frumpty to denote the number 100, and say it isn't defined in terms of other numbers. But why not use the word hundred, which is a perfectly suitable word for exactly that number. Why is a dozen special opposed to, say, a million?
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Because "million" just fits into the sequence of numbers. You can have a one-million-three-hundred-thausand-and-twelve. But you don't get three-dozen-ty-and-four or something like that.

You could. And you could have "frumpty", but you don't. ;)

So, I think words like "dozen" or "score" or "googol" are special. And I think there is a difference between "dozen" and "score" vs. "googol" or "gross", too.

I am not seriously arguing that that makes "score" the largest number", of course.
 
"Score" really is used just like "million". The obvious example is "four score and seven years ago" from Lincoln's Gettysburg Address. Another example is the biblical life scan of "three score and ten".
 
how abut numbers raised to the power of loads surely the heighest number is the next logical step currently (using the ISO scale) you have
bucket^loads
cart^loads
shed^Loads
bus^loads
Boat^loads
What comes next? Surely it must be the BIGGEST thing EVER? simliarly (or even similiely) is there any thing smaller than a Gnats Chuff?
 
No "Look around you" link?

/it's like you people have never been on the internet before
 
The largest number on this board is (X+1) where X is the largest number stated anywhere else on this forum. I win!
 
Mister Earl said:
The largest number on this board is (X+1) where X is the largest number stated anywhere else on this forum. I win!
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Not if I call the cardinal Aleph-zero, it isn't. :p Aleph-zero + 1 = Aleph-zero.

So, I'll call 2X where X is the largest number stated anywhere else on this forum. Since I stated Aleph-zero, I get Aleph-one.
 
Smallest Number = One
Middle Number = Two
Largest Number = Many

Linky
The Piraha of the Amazon have almost legendary status in language research. They have no words at all for number. They use only only three words to count: one, two, many. To make things confusing, the words for one and two, in Piraha, are the same syllable, pronounced with a falling or rising inflection.

And to make things really difficult, the word for one can sometimes mean "roughly one", and the word for two can sometimes mean "not many".
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The largest number in the world is a number 4 I once found when I was traveling. It was 2000 feet tall.
 
Cantor would disagree.
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You theif. I said that already.

Anyway, the largest number is 45,000,000,000, however mathematician speculated there are even higher numbers
(45,000,000,001)?
 
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Cabbage said:
You'll get something bigger than Aleph-zero, but it won't necessarily be Aleph-one.
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Why will you get something bigger than Aleph-zero? The procedure for mapping powers of two on to the cardinal numbers is fairly straightforward - you just count an additional 2^(i-1) elements to add the ith dimension. Given that you can map the elements of a set of size 2^n on to the cardinal numbers for any value of n, then 2^Aleph-zero = Aleph-zero.

Dave
 
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Dave Rogers said:
Why will you get something bigger than Aleph-zero? The procedure for mapping powers of two on to the cardinal numbers is fairly straightforward - you just count an additional 2^(i-1) elements to add the ith dimension. Given that you can map the elements of a set of size 2^n on to the cardinal numbers for any value of n, then 2^Aleph-zero = Aleph-zero.

Dave
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I'm not absolutely positive I'm following what you're saying, but I think you're defining 2^Aleph-zero by ordinal arithmetic (which is fine, of course). As an ordinal, 2^Aleph-zero is defined as the supremum of {2^n:n is a natural number}. Of course, that's just aleph-zero (or omega, using the ordinal name).

Cardinal exponents are different, though. 2^Aleph-zero is defined as the cardinality of the set of all functions from aleph-zero (the natural numbers) to 2 (where 2={0,1}). Or, in other words, 2^Aleph-zero is defined as the cardinality of the power set of natural numbers. This is strictly larger than aleph-zero (and may be strictly larger than aleph-one).
 
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