Is googolplex almost infinity?

[Dundasbro]

?!

 

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))?

I apologise for my ignorance, since i do only have any physics education being 15, and did not realise what you were referring to as "c". Also i'm sorry but i don't know enough on the subject to answer the question... I am beaten :lol: You win

[alxian]

i only meant to put the question into context

 

 

if infinity can't be quantified how about another theoretical infinity, c

 

if one can't compare anything to infinity and one cannot travel at c are they similar?

 

not a fair question i suppose but soemthing to think about, because like 50mph, the speed of sound, escape velocity, man will travel faster than c its just a matter of time, how is still theory. while we will never be able to quantify infinity simply keep finding stuff we can quantify that bigger and bigger and bigger, never comparable to infinity but pretty big numbers.

[CraigD]

… if infinity can't be quantified …

Alxian is stating here what’s appears to have become as a consensus fact in this thread – that infinity can’t be quantified. I believe this is misleadingly false.

 

I hold with the idea that what is meant by something being quantifiable in this context is perhaps better named formalized – that is, a collection of rules exist that allow us to represent the thing with symbols, and perform useful (or even useless) transformations of those symbolic representations.

 

For most of western history, infinity was considered unquatifiable – that is, using a symbol for it in any formal system was considered suspect, and avoided. The Greeks, Newton, etc. all were careful to never write expressions like “infinity + 7” or “infinity / 10”, just as we common-sensically avoid writing expressions like “1.5 intact marbles”. Infinity, though related to numbers of various kinds, was not itself a kind of number, and thus not to be used in numeric expressions.

 

Around 1870, mathematicians had had enough of this restriction, and began in earnest to try building a formalism for infinity. Perhaps to avoid confusion with its older meaning (or endlessly looping discussion threads!), the term “transfinite” was usually used in place of “infinite”. There’s widespread agreement that Georg Cantor was the superstar of transfinite math (or at least was, until he went pretty much crazy in the 1890s, and started dividing his time between Math, in-patient mental health therapy, theology, and conspiracy theories about Shakespeare).

 

To make a long and technical story short, Cantor and others were pretty successful in building a rich and useful, though esoteric, formalism for transfinite numbers. In this formalism, transfinite numbers can be compared as meaningfully as integers, that is, one can evaluate the truth of an expressions such as “A=B” or “A>B” where A and B are transfinite. When, as various poster in this thread have done, we assert that expressions like “infinity + 1 = infinity” is true, we’re relying on this formalism, which also describes expressions of both finite and transfinite numbers. When we use terms like aleph-null, aleph-1, or any an infinite collection of aleph-__s, were using terms from this formalism. Even if this makes little intuitive, physical sense to a reader, the formalism is sound and useful.

 

Like nearly every non-trivial formalism, transfinite math has plenty of unsolved problems, the most famous, I’d say, being the Continuum hypothesis.

[pgrmdave]

I think that one important consideration is the infinite amount of infinities. Consider the infinity of numbers between 0 and 1. Now consider that there must be an equal infinity between 1 and 2, because the numerical distance between those numbers is equal, thus the infinite amount of numbers fitting there must be the same. SO, the infinity of numbers from 0 to 2 must be exactly twice as great an infinity. While both infinities are beyond quantification, one is greater than the other.

[CraigD]

... Now consider that there must be an equal infinity between 1 and 2, because the numerical distance between those numbers is equal, thus the infinite amount of numbers fitting there must be the same. SO, the infinity of numbers from 0 to 2 must be exactly twice as great an infinity. While both infinities are beyond quantification, one is greater than the other.

Though counter intuitive, where A is a transfinite number, A+A=A.

 

To have a transfinite number B > A, there must be something different about the way one counts the members of infinite sets to arrive at A and B (In other words, the Cardinality of the sets must differ). For instance, the cardinality of the set of rational numbers between 0 and 1 is less than the cardinality of the set of real numbers between 0 and 1, but not less than the set of rational numbers between 0 and 2, because the way you can count the rational numbers between 0 and 1 is the same as the way you can count the rational numbers between 0 and 2, but not the way you can count the real numbers between 0 and 1.

 

If you want to assail and insult your intuition with some transfinite math foundations, try checking out some wikipedia articles involving countability, or similar texts.

[Qfwfq]

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...

It's a lot more subtle than that, and you shouldn't be blaming others for not understanding.

 

Although no number is close to infinity, "closer to" also means "less far from" so the question does make sense (distance defined as modulus of difference) but the answer is very, very subtle.

 

infinity - n = infinity

 

How much is infinity - infinity?

[Qfwfq]

if infinity can't be quantified how about another theoretical infinity, c

 

if one can't compare anything to infinity and one cannot travel at c are they similar?

I would leave c out of the matter. We are talking about mathematics here.