Is the Smallest Unnameable Number a Paradox?

[Galteeth]

 

[CompuChip]

Actually I thought this one was funnier.

 

[humanino]

Biggest named number is Googolplex

 

[Cryptonic]

Biggest number is ZERO.

 

[CompuChip]

Or sup R?

 

[leroyjenkens]

The biggest number is infinity minus one.

 

[Integral]

The biggest number is infinity minus one.

Are you sure? how about infinity - .5 ... no wait...maybe infinity - .1 ... no wait...

Gee maybe there is NO biggest number.

 

[Topher925]

Are you sure? how about infinity - .5 ... no wait...maybe infinity - .1 ... no wait...

Gee maybe there is NO biggest number.

No, its infinity minus one over infinity.

 

[leroyjenkens]

Are you sure? how about infinity - .5 ... no wait...maybe infinity - .1 ... no wait...

Gee maybe there is NO biggest number.

You're right. My mistake.

Infinity minus one is the largest WHOLE number.

 

[Hurkyl]

Biggest named number is Googolplex

What about constant[/url]?

 

[DaveC426913]

Second for Graham's number.

Infinity is a concept, not a number. Graham's number has the distinction of being the largest number ever used in a serious work of math.

And it is large indeed. In fact, it leaves 'large' lying upside-down on the dirt track, feet in the air with one shoe off and its frillies billowing in the breeze.

 

[Redbelly98]

You're right. My mistake.

Infinity minus one is the largest WHOLE number.

That would be true if infinity were a whole number, but it isn't.

 

[Jimmy Snyder]

It's 42[/size]

 

[Hurkyl]

Infinity is a concept, not a number.

While probably true given some interpretation of these words, there are several number systems that have numbers named "infinity" or some variation thereof.

 

[Hurkyl]

It's 42[/size]

That's not a big number: that's a big numeral.

 

[CompuChip]

It's 42[/size]

No no ,you got it all backwards!

(And we're back at post #1)

 

[Jimmy Snyder]

What about constant[/url]?

You're forgetting Jimmy's constant J equal to Graham's constant plus one. There's a mathematical theorem that makes use of Jimmy's constant in the form J - 1.

 

[jobyts]

Jimmy's back to mine-is-bigger game.

I think jobyts constant is bigger than any of other constants. It's defined as Pi without the dot.

 

[DaveC426913]

You're forgetting Jimmy's constant J equal to Graham's constant plus one. There's a mathematical theorem that makes use of Jimmy's constant in the form J - 1.

You kill me.

 

[humanino]

What about constant[/url]?

Sorry, I meant "biggest number known to humanino before Hurkyl's post". Thanks.

 

[Galteeth]

Sorry, I meant "biggest number known to humanino before Hurkyl's post". Thanks.

Well, the thread is a joke, but it is an interesting question, as in if there's a semantic limit to the ability to coherently represent a number. In other words, what would be the biggest real number hypothetically represented by all the possible symbols imbued with maximum semantic sense (by semantic sense, i mean, we can say G64 in regards to graham's number and that can have some semantic meaning, but surely at ooe point there's an absolute limit that would actualy be representable?)

 

[CompuChip]

Isn't the point of mathematics that there isn't?
There simply are infinitely many numbers, so whenever we need to represent them we can always find a way to express them mathematically, like
$$10^{10^6}, 3 \uparrow\uparrow\uparrow 64 \text{ or } x$$

Or am I really misunderstanding your question, Galteeth?

 

[Jimmy Snyder]

Well, the thread is a joke, but it is an interesting question, as in if there's a semantic limit to the ability to coherently represent a number. In other words, what would be the biggest real number hypothetically represented by all the possible symbols imbued with maximum semantic sense (by semantic sense, i mean, we can say G64 in regards to graham's number and that can have some semantic meaning, but surely at ooe point there's an absolute limit that would actualy be representable?)

Let A be the set of all positive integers that cannot be represented by all the possible symbols imbued with maximum semantic sense. This set must have a smallest element. That element has just been represented by symbols imbued with semantic sense. Therefore, the set A must be empty.

 

[Redbelly98]

Ha ha, I just got around to watching this. The bits at the end were pretty good too.

 

[Borek]

There's a mathematical theorem that makes use of Jimmy's constant in the form J - 1.

Strangely, same can be said about B-2.

 

[jobyts]

Let A be the set of all positive integers that cannot be represented by all the possible symbols imbued with maximum semantic sense. This set must have a smallest element. That element has just been represented by symbols imbued with semantic sense. Therefore, the set A must be empty.

I remember there was a paradox for this, cannot think of the name. It says something like,

"What's the smallest positive integer that cannot be expressed in less than a billion words?"

If you name that number, we just expressed in a smaller form, and it becomes a paradox.