The largest number?

L

Lookingfor...

Registered Member
Hello. I believe there is already a thread about this, however I cannot find it.

Numbers increase as follows:

0-9 (Units)
10 (Tens)
100 (Hundreds)
1000 (Thousands)
10,000 (Ten-Thousands)
100,000 (Hundred-Thousands)
1,000,000 (Millions)

Surely what follows is Ten-Millions, Hundred-Millions, Thousand-Millions, and so on? So then, there is some contention between the United States and Great-Britain. I maintain a Billion has twelve zero's, and a trillion twenty-four...

1,000,000 (A Million)
1,000,000,000,000 (A Billion) (A Million Million)
1,000,000,000,000,000,000,000,000 (A Trillion)

If infinity is the largest number, what of infinity plus one?
 
NotEinstein said:
As the article states, Graham's number is the largest number ever used in a mathematical proof.
Click to expand...
Got it

As I said I didn't go into it to deeply but kept the link for future reference when I got around to it. Never did

At least now I know I can add1 to Graham's Number to get a bigger number

The only way I can picture obtaining the biggest number is to set some sort of boundaries about what is counted

I would suggest if you break the Universe down to the smallest units everyone agrees exist. Count them - nothing left to count - biggest number

:)
 
technically, there is no such thing as the largest number. it's a number that's just compounded (repeat).

if you have a million one dollar bills, that's still one dollar bills a million times.
 
Mathematicians & science-oriented folks regularly use millions & billions conversationally, less often using trillions.

They tend to use exponential notation beyond billions, although English & various other languages have words for such values.​

It is politicians, news writers, & ordinary people who use regularly use words like quadrillions & words for larger numbers.
 
Dinosaur said:
Mathematicians & science-oriented folks regularly use millions & billions conversationally, less often using trillions.

They tend to use exponential notation beyond billions, although English & various other languages have words for such values.​

It is politicians, news writers, & ordinary people who use regularly use words like quadrillions & words for larger numbers.
Click to expand...
beyond millions is gazillions; that's why i use exponents
 
Lookingfor... said:
Surely what follows is Ten-Millions, Hundred-Millions, Thousand-Millions, and so on? So then, there is some contention between the United States and Great-Britain. I maintain a Billion has twelve zero's, and a trillion twenty-four...

1,000,000 (A Million)
1,000,000,000,000 (A Billion) (A Million Million)
1,000,000,000,000,000,000,000,000 (A Trillion)
Click to expand...
It used to be the case, I believe, that in Great Britain, a new name was given for every extra power of $$10^6$$. So, we had:

1,000,000 (million)
1,000,000,000,000 (billion)
1,000,000,000,000,000,000 (trillion).

Although some people might argue that a trillion should be a billion billion rather than a mere million billion.

The number 1,000,000,000 would be referred to as "1 thousand million".

Usage in the United States was different. It used powers of $$10^3$$ instead:

1,000,000 (million)
1,000,000,000 (billion)
1,000,000,000,000 (trillion)

So, in particular, the number 1,000,000,000 would have been called a billion in the US, and one-thousand million in the UK.

---
My impression is that this dispute is largely settled now, and the Americans seem to have got their way, at least for most people.

Scientists tend not to worry about naming numbers larger than the millions anyway, since it is usually shorter just to use power-of-ten notation. There's no ambiguity if you just write $$10^3, 10^6, 10^9, 10^{12}$$ etc.

If infinity is the largest number, what of infinity plus one?
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This is the problem with infinity. Some would say that infinity is not really a number, as such, but rather the limit of some kind of counting process. There's an entire area of maths that deals with so-called transfinite numbers.

It turns out that, depending on how you define things, there can be a difference between $$1 + \infty$$ and $$\infty + 1$$. The first indicates the number that comes a infinite number of numbers after the number 1, while the second indicates the number that comes next after infinity; these are not the same thing.

Under the usual rules, it turns out that $$1 +\infty = \infty$$ (because if you add infinity to anything finite you get infinity), but $$\infty + 1$$ is the first "transfinite" number (because we start with infinity and then make something bigger).
 
James R said:
Under the usual rules, it turns out that $$1 +\infty = \infty$$
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This is meaningless. You can't add to the $$\infty$$ symbol. It's not defined.

There are a couple of ways to do arithmetic with infinity. One is with ordinals, the other with cardinals.

What's interesting is that in the transfinite ordinals, addition is not commutative.

For example, the first transfinite ordinal is called $$\omega$$. It's the ordinal that comes after all of the finite ordinals $$0, 1, 2, 3, 4, \dots$$

$$\omega$$ represents the order type of the finite ordinals. The ordinal $$\omega + 1$$ consists of all the natural numbers followed by $$\omega$$. It looks like

$$0, 1, 2, 3, 4, \dots, \omega$$

Now this order type has a first element and a last element. It's a different order type than that of the natural numbers.

On the other hand the order type $$1 + \omega$$ is just $$\omega$$ with an extra element stuck on at the beginning. It looks like

$$x, 0, 1, 2, 3, 4, \dots$$

where 'x' is just some extra symbol. We can see that this order type is identical to the order type of the natural numbers.

So $$1 + \omega \neq \omega + 1$$

On the other hand, addition of transfinite cardinals does happen to be commutative.

This is why mathematicians are very precise when they speak of infinity. The symbol $$\infty$$ does not have the meaning you are ascribing to it.

$$\infty$$ is not regarded as a transfinite number.

ps --

James R said:
It turns out that, depending on how you define things, there can be a difference between $$1 + \infty$$ and $$\infty + 1$$. The first indicates the number that comes a infinite number of numbers after the number 1, while the second indicates the number that comes next after infinity; these are not the same thing.
Click to expand...

Oh you already noted this. But $$\infty$$ isn't the right symbol here. So my post is hereby downgraded from a correction to a quibble.
 
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Okay. But perhaps the largest number is nine, or ten.

The decimal system has only ten sybols: 0-9. After this a column is added to the left, and the symbols are reused. First zero, then one, then two, etcetera

Symbol-Position
9-10
8-9
7-8
6-7
5-6
4-5
3-4
2-1
0-1
 
Lookingfor... said:
Okay. But perhaps the largest number is nine, or ten.

The decimal system has only ten sybols: 0-9. After this a column is added to the left, and the symbols are reused. First zero, then one, then two, etcetera

Symbol-Position
9-10
8-9
7-8
6-7
5-6
4-5
3-4
2-1
0-1
Click to expand...
But 20 is larger than any of the numbers you mentioned, so 9 or 10 can't be the correct answer.
 
Lookingfor... said:
Okay. But perhaps the largest number is nine, or ten.

The decimal system has only ten sybols: 0-9. After this a column is added to the left, and the symbols are reused. First zero, then one, then two, etcetera

Symbol-Position
9-10
8-9
7-8
6-7
5-6
4-5
3-4
2-1
0-1
Click to expand...
I don't know why but I am getting a distinct urge to Spinal Tap.
;)
 
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