almost infinity

vikasj007

well, yesterday i was talking to my friend, and during the conversation he used the term "almost infinity". though he intended to refer to something very large, but he got me thinking.

what is "almost infinity"?

or let me rephrase it in a beter way.

is it correct to use the term "almost infinity", to describe anything, or any value, and what would it signify.

Gokul43201

There is no absolute largeness for a number. A number can only be large compared to something else (eg: compared to 1).

'Almost infinity' IMO is very poor language. No real number is a greater fraction of "infinity" than any other.

[tex]\lim _{N \rightarrow \infty}\frac{n1}{N} = \lim _{N \rightarrow \infty}\frac{n2}{N}~~~~ [/tex] for all real n1, n2.

Hurkyl

The phrase is often used to indicate that the parameter is large enough such that the behavior is adequately close to the limit.


For example, if you're working on a statistical problem identifying the possibility of something happening, and its probability is 1/10^n, then one might say that 100 is "almost infinity" (or some similar phrase) to indicate that the corresponding probability is so small, it can be treated as 0 (the limit) for the purposes of the problem.

Gokul43201

So, is "almost infinity" an accepted terminology ?

I would have used different words !

dextercioby

No,missused words.The best example i could come up with is in statistical physics,where one deals with virtual statistical ensembles,which,by definition,mean an infinite number of identical statistical systems.However,our resoning provides the correct answers by dealing with an arbitrary large,yet finite,number of such systems.
Take it as a language thing:"infinite" is an adjective that does not have degrees of comparison.Therefore it's not "relative".


Daniel.

Hurkyl

You know mathematicians and our sense of humor. It's simply more fun to say it that way. (I myself have said things like "Where infinity = 10") Of course, I would never say things in such a way except around people where there was no chance of misunderstanding.

Gokul43201

Gotcha ! It's an inside thing.

SGT

Since most electrical components have a tolerance of 10%, electrical engineers consider that a measure that is ten times greater than another is infinitely greater.

Icebreaker

Maybe he was talking about infinite sets.

scarecrow

No. "Almost infinity" is a paradox. Infinity by definition is no end or no limit, so saying "almost infinity" implies you are near infinity, when that is impossible. You can never say almost infinity. That just contradicts the definition of infinity.

Hurkyl

Mathematically, we like to use definitions somewhat more precise than that.

K.J.Healey

What is the mathematical definition of "almost"?
I would say assuming infinity is talking about quantity, then since every other possible number is infinity away from infinity, there could exist no number that was "almost" infinity. Every number is therefor equidistant from infinity and that distance is maximum, leaving no room for a comparison of "almost" becuase there would be no lower numbers by which to compare.
I love/hate these types of arguments. Its always semantics...

Hurkyl

Almost infinity is an informal term, not a formal one, so it doesn't really have a definition.

(However, things like "almost everywhere" or "almost surely" are formal terms and have definitions)

BigStelly

[QUOTE=Healey01]What is the mathematical definition of "almost"?

Good point..... you cant be almost to infinity without reaching it, if you define almost as within 1,10,100,.0000000000001 either way you are at infinity by definition of infinity. Your freind probably meant something very large that would be hard to think of in mathematical terms but was not infinite(nor even close by the definition of infinity)

vikasj007

well, ofcourse i know that it is impossible to attain infinite value for anything, so it cannot possibly be correct to term something as infinite, but what i meant was that as it is said that even if you add or subtract anything from infinity, you'll still get infinity. so is anything close to infinity any different from infinity??

K.J.Healey

I thin we all argued that you CANT BE CLOSE to infinity. To think of (infinity-1) as anything more/less than infinity is wrong. Is 27 close to 27? No, it IS 27. The only thing that defines a number from another is a difference between them. The distance between infinity-10 and infinity is infinitely small, and due to limit theory goes to zero.

A similar argument I had with someone was whether or not .9999 repeating was the same as the number 1. I argued it was, there is no difference between the numbers (difference in the mathematical sense) therefor they are the same number.

Icebreaker

There's infinite sets.