# What's the biggest number that has a name?

That was a good explanation, AHunter3. For Graham’s number- whoo boy, I don’t have those years of mathematical education yet.

I think you’ve opened yourself up to a Berry Paradox there.

The number thing others have answered more or less accurately. I just want to pick a bit of a nit about the source of the name “google”. Yes, the gloss of googol as a large number is intended (with respect to the amount of results returned), but it also refers to google, a deprecated form of goggle: “To turn the eyes to one side or other, to look obliquely, to squint”. That is, it looks at a lot of different things in all sorts of directions.

How about the second Skewes Number which equals 10[sup]10[sup]10[sup]10[sup]3[/sup][/sup][/sup][/sup]?

Compared to Skewes Number[sub]2[/sub] a googolplex (10[sup]10[sup]10[sup]2[/sup][/sup][/sup]) is virtually zero.

I have way too much time on my hands, it would seem.

OK, here’s one you could count to without hitting unnamed numbers (if it weren’t for mortality and the heat death of the universe and stuff like that):

Still expressible in exponential notation. Not a contender.

It’s easier if you use bigger numbers. Try this on for size:

Aleph-null bottles of beer on the wall,
Aleph-null bottles of beer
Take one down and pass it around
Aleph-null bottles of beer on the wall

At least, if you accept “aleph-null” as a number. But if you do, then it’s still not the largest number, since you’d then also have to accept aleph-one, aleph-two, aleph-centillion, etc., and there are other “numbers” which are bigger than any aleph, and so on.

Nobody would do that. Because NurseCarmen’s number is bor’s number times two.

Well, as we know, if we divide 1 by smaller and smaller numbers, we get larger and larger numbers. So we divide one by zero for a very, very, *very * large number.

“But that is mathematically impossible!”, you would say.

Ahhhhh, but here’s the beauty of it: We take the result and subtract 1.

((1/0) - 1)

And we name it “plynck’s constant”.

Yep, got it all figured out, and before dinner, too

Meh. After the first duodecillion beers or so, who gives a crap anymore?

Are there any rational numbers not expressible in exponential notation? Irrational numbers being not expressible at all in digits, only their approximations.

And we really need to find help for AHunter3

When you’re dealing with large numbers, “expressible” seems to be taken as a synonym for “intelligibly expressible”. Graham’s number, for instance, is expressible in exponential notation, but not in any meaningful way.

Infinity is certainly an established name.

A Googleplex is probably the highest commonly known number.

Graham’s Number appears to be the highest number that’s ever been actually used.

The Moser appears to be the highest definable number.

999 vigintillion 999 novemdecillion 999 octodecillion 999 septemdecillion 999 sexdecillion 999 quintdecillion 999 quattuordecillion 999 tredecillion 999 duodecillion 999 decillion 999 nonillion 999 octillion 999 septillion 999 sextillion 999 quintillion 999 quadrillion 999 trillion 999 billion 999 million 999 thousand 999 is the highest number that could theoretically be counted to (as in all numbers less than it would have a name).

But infinity isn’t a number.

How do you figure? It looks like AHunter3 has counted quite a bit higher than you…

Correct me if I’m wrong, but I’m pretty sure the unmodified word “number” has no formal definition in mathematics, so you can’t really pin down whether something is or is not a “number”—it depends on what kind of numbers or what set of numbers you’re talking about.

I think most of the posts so far have assumed the OP was asking about the biggest real number—a natural assumption, since the set of real numbers (or perhaps some subset thereof) is what most of us think of when we think of “numbers.” And yes, infinity is not a real number. But if you allow things like transfinite numbers (as Chronos mentioned), that’s a whole new ball game, and you can easily get “bigger” numbers than any of the real numbers mentioned.

Little Nemo is correct if we confine ourselves to officially accepted names. The other names are considered logical extensions of the official naming convention (“considered” meaning "by people other than just me, i.e., I didn’t just make them up or anything

I have no idea why the official named series stops at the vigintillion mark.

But it doesn’t refer to anything specific; in fact, I don’t think it means anything out of context.

It may the highest number that anyone’s bothered to define, but simply definining a k-Moser as (Moser)[sup]k[/sup] gives you a lot of larger, defineable numbers.

Chronos did add the proviso that you need to accept transfinite “numbers” as numbers - I don’t. The don’t obey rules of addition, subtraction etc. as far as I can tell or the rule of succession that tells us how to form members of the set.

I wouldn’t be surprised to be wrong about this but that’s my story until a mathematician comes along to show that such entities do follow such rules.