What is the largest number that can fit in x units of space?

[withdrawn]

This makes no sense.

Sure it does; Any value can be divided into an infinite amount of fractions.

 

[T@P]

yes but that does not prove that 1 = infinity. all it shows is that there are an infinite number of points in a segment (basically the definition of the space you are in) I don't see how this applies really...

 

[Rogerio]

Mathematically any given line segment is composed of an infinite number of points.
Given the existence of a plank length, it would seem to resolve to a specific number.

A line segment is not a real object! Plank doesn't apply!

Is a line segment that I draw any less real than say a square or a triangle?
In other words -> Why does Plank not apply?

What you draw is just a physical representation of a mathematical line segment. And it's not the mathematical line segment.
Plank applies to physical objects, not mathematical objects.
Simple like that.

The same way, despite Plank, there is an infinite amount of real numbers in the [0,1] interval...:-)

 

[Ba]

Yes but keep adding on points to make the interval [0,2]. That's still infinity. Is one bigger than the other?

 

[Rogerio]

Yes but keep adding on points to make the interval [0,2]. That's still infinity. Is one bigger than the other?

Both intervals have infinite points inside, and you can binuvocally map the [0,1] into the [0,2] without problems.
And this has nothing to do with Plank...:-)

 

[NoTime]

What you draw is just a physical representation of a mathematical line segment. And it's not the mathematical line segment.
Plank applies to physical objects, not mathematical objects.
Simple like that.

The same way, despite Plank, there is an infinite amount of real numbers in the [0,1] interval...:-)

The comments relate to the distinction between the virtual playground and the actual playground.
So your point is... that you did not read the rest of the thread?

 

[Rogerio]

The comments relate to the distinction between the virtual playground and the actual playground.
So your point is... that you did not read the rest of the thread?

Of course I did. By the way, at your last comment you had quoted the following:
"Originally Posted by Gokul43201
You are confusing a mathematical axiom with an assumption involved in a physical theory."

As you should have noted, it's about distinction between the virtual and the real playgrounds, too.
It seems you remain a bit lost...:-)

 

[Gokul43201]

1 = infinity

0.000(insert infinite amount of 0's here)000.1 to 1.0

Same applys to every other number or value so why even discuss it?

Let me refine Hurkyl's objection.

"This makes no mathematical sense."

 

[T@P]

i fully agree with goku43201

 

[NoTime]

It seems you remain a bit lost...:-)

Can't argue with that
But you could probably drop the "bit"

I still think Zeno was right. The bounded infinity is illogical in its own frame.

 

[Noticibly F.A.T]

Has anyone actually answered the question at the start or this topic? I have, and i think 3 others did. Let's hear more answers, instead of petty squabling over infinity.

 

[Ilm]

Simplify the question and put an effort to make it understandable. You'd receive answers that will satisfy.

Most of the readers didnt get the whole point, precisely, of what to do... which was your job, now we can't even find what to answer!

 

[Noticibly F.A.T]

I didn't ask the question. I can't remember/i am too lazy to find out who did.

 

[NoTime]

Most of the readers didnt get the whole point, precisely, of what to do...

Exactly
Originally the "infinity" was an undefined answer for an undefined question.
That part just kind of got lost along the way.

 

[T@P]

sorry for not simplifying the question...

well ill do my best to re-state it here.

Assuming that every number symbol, *anything* that you write has a given "area", you want to write the biggest number with the smallest area.

Note also that your bits of "area" can be arranged any way you want, and also that i sort of came up with this idea randomely and that i honeslty don't know the answer or if the question makes sense. but what i am looking for is some *proof* or convinving argument for one particular method is right.

I hope you arent all confused yet, but just to state an obvious example, 9^9^9 would occupy 3 "areas" (the '^' is not written by hand). I actually have no idea if this is the "biggest number or not, but it is a candidate. Hope i made it clear Ilm :)

 

[Noticibly F.A.T]

How about, writing ther number 9, then taking it to the power of 9, but instead, but the other 9 on its side, and then another 9, upsidedown, and then anotherone, so they are on top of each other, yet still only take up one space (on paper anyways)

 

[T@P]

hmm it is an idea, but for now I am sticking to each number has its own "area", and all areas are equal. And even then, by sticking lots of 9's together, you basically get an 8, so i don't really see how it would help :)

 

[NoTime]

I hope you arent all confused yet, but just to state an obvious example, 9^9^9 would occupy 3 "areas" (the '^' is not written by hand). I actually have no idea if this is the "biggest number or not, but it is a candidate. Hope i made it clear Ilm :)

Sorry, Absolutely no improvement

 

[MiGUi]

1 \over \Lambda with Lambda = cosmological constant

 

[T@P]

An example if a number would be 9^93 this number occupies 3 "areas" because there are three numbers written down. It is not the biggest number of three areas because 9^9^9 is bigger and also occupies three. So the question was, with 3 "areas' what is the biggest number? or for that matter, with n areas?