Is googolplex almost infinity?

[alxian]

thus it is rational to take the statement at face value

 

to add one is to get closer and not get further away from a greater number like infinity.

 

it is better to take a step knowing you will never reach your goal than to stand still. claiming i move as much as you who choose to move do.

[Dark Mind]

in·fi·nite ( P ) Pronunciation Key (nf-nt)

adj.

Having no boundaries or limits.

Immeasurably great or large; boundless: infinite patience; a discovery of infinite importance.

Mathematics.

Existing beyond or being greater than any arbitrarily large value.

Unlimited in spatial extent: a line of infinite length.

Of or relating to a set capable of being put into one-to-one correspondence with a proper subset of itself.

 

n.

Something infinite.

 

 

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[Middle English infinit, from Old French, from Latin nfntus : in-, not; see in-1 + fntus, finite from past participle of fnre, to limit. See finite.]

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infi·nite·ly adv.

infi·nite·ness n.

Synonyms: infinite, boundless, eternal, illimitable, sempiternal

These adjectives mean being without beginning or end: infinite wisdom; boundless ambition; eternal beauty; illimitable space; sempiternal truth. See also synonyms at incalculable

Usage Note: Infinite is sometimes grouped with absolute terms such as unique, absolute, and omnipotent, since in its strict mathematical sense infiniteness is an absolute property; some infinite sets are smaller than others, but they are no less infinite. In nontechnical usage, of course, infinite is often used to refer to an unimaginably large degree or amount, and in these cases it is acceptable to modify or compare the word: Nothing could give me more infinite pleasure than to see you win. Withdrawing the troops would create an even more infinite set of problems for the coalition. ·Note that unlike other incomparable adjectives, infinite when used in its strict literal sense cannot be modified by words like nearly, since quantities do not approach infinity by degrees. This constraint, too, can be ignored when the word is used simply to refer to a very large number: You need a nearly infinite amount of patience to do the job.

This is my last post in this thread... We're going in circles now, I'm done...

[Buffy]

We're going in circles now, I'm done...

Of course you can go in a circle infinitely! How appropriate!

 

Cheers,

Buffy

[Tormod]

This is my last post in this thread... We're going in circles now, I'm done...

 

Sure you are. :rant:

[pgrmdave]

Now, are each of these posts getting us closer to an infinite thread :rant:

[Qfwfq]

C'mon Dark Mind, don't get frustrated! If you go, you'll only miss a lot of fun! :eek:

 

For your first sentence; that's not what I said or tried to imply.

I think it was someone else. It was a long time ago!

 

For the question; actually alex said that it is probably close enough to the number of molecules in our universe to be represented by every individual molecule in our universe.

Have you ever counted the number of quarks and gluons in a hadron?

 

I think you misread his post...

Caught me there!!! :wave:

 

Aw, shucks, I must have read it quick, along with the other posts, and confused it with them. :rant:

 

I can't believe you just wrote that!

I think you missed the subtlety I put into my answer: "Slightly! It's only (googolplex -1) closer to infinity than 1 is."

 

Saying anything is or can be close to infinity implies it's quantifiable...

What do "close" and "far" mean, in mathematics? It's a matter of defining a metric. Are the cardinalities of N and R quantities? Is the limit of a quantity a quantity?

 

IT'S A CONCEPT. Nothing is near infinity.... That's the whole idea of infinite :eek:. None of these numbers are even a million googolplex away from infinite!

I disagree. What's infinity - n?

[Tormod]

I disagree. What's infinity - n?

 

Hm. To me this is like asking, "what is blue - fish?"

[Qfwfq]

In terms of cardinality: What is the cardinality of the set of all natural numbers excepting those less than n?

 

Answer: same as the cardinaliy of N.

 

This is a case in which the definition "Of or relating to a set capable of being put into one-to-one correspondence with a proper subset of itself" from Dark Mind's dictionary applies.

 

In the sense of limits: If lim(x--a) f(x) = infinity, what is lim(x-->a) (f(x) - n)?

 

Answer: same as lim(x--a) f(x).

 

This is a case in which the definition "Existing beyond or being greater than any arbitrarily large value" from Dark Mind's dictionary applies.

[Qfwfq]

Nothing is near infinity.... That's the whole idea of infinite :rant:. None of these numbers are even a million googolplex away from infinite!

I realize I must have got your meaning here wrong DM, sorry, it didn't match up to me but I thought you meant that it's meaningless to say either near or far from infinity.

 

Of course, all these numbers are infinitely "far" from infinity, their distance of from infinity is infinite.

[Dundasbro]

Infinity is never ending, so a googleplex isn't even close to infinity cos there isnt a "close" to infinity...

[alxian]

as 5 is closer to 10 than 2 so too is a googolplex closer to infinity than 1

 

 

how did this thread get to 5 pages in lentgh without mentioning milton sirotta?

 

Googolplex: "Coined at the age of nine by Milton Sirotta, nephew of Edward Kasner"-- American mathematician.

[Dundasbro]

as 5 is closer to 10 than 2 so too is a googolplex closer to infinity than 1

ARRRRRRRGGHHHHHHHH!!!! :lol: :eek: :) :ud:

No, that is completely wrong, infinity isn't close to any number therefor no number is "closer" to infinity than another. A number is a set amount, 1 is 1, 2 is 2... And so on. What people in this thread can't understand is that infinity is not a set amount, it is never ending and nothing is close to it because there is always something bigger and there is always something smaller. There is such a thing as being infintisimally (ignore the spelling please) small...

[alxian]

No, that is completely wrong,

 

how so?

 

you're saying infinity is intangible, fine, but by definition it is greater than 10 and thus greater than zero

 

infinity > 10 > 0

 

so

 

10 > 5

 

5 > 2

 

but 10 is much greater than 2 and is relatively less great compared to 5 than to 2

 

but infinity > gp > 10 > 5 > 2 > 1 > 0

 

so... even if infinity is intangible its still greater relatively than a gp compared to 10 or 1 even if the difference is less great than 10 > 5 relative to 10 > 2. even if that difference equally intangible intellectually you know that its there, and intellectually could be quantifiable if either infinity or the difference between infinity vs a gp/10/1 could be quantified an infinitesimally small amount but an amount none the less.

[Dundasbro]

Point taken, but i still believe that the original question "Is googolplex almost infinity?" is a completely useless question altogether, my point was that nothing can be close to infinity because it is intangible. And a set number can not be close to infinity.

[alxian]

which is a much better position to take, yes.

 

are you one then who would say c is an intangible and an absolute man will never conquer?

[Dundasbro]

are you one then who would say c is an intangible and an absolute man will never conquer?

Not so sure about the "c" thing. But if memory serves "Absolute" means perfect, and no human is perfect (it's an intangible expectation just like infinity) So no, I don't believe that an absolute man will conquor

[alxian]

?!

 

are you one then who would say c (speed of light in vacuum) is an intangible and an absolute, that human beings will never conquer (travel FTL (faster than light))?