- #1

- 161

- 0

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.

- Thread starter vikasj007
- Start date

- #1

- 161

- 0

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.

- #2

Gokul43201

Staff Emeritus

Science Advisor

Gold Member

- 7,051

- 18

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.

'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.

Last edited:

- #3

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

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.

- #4

Gokul43201

Staff Emeritus

Science Advisor

Gold Member

- 7,051

- 18

So, is "almost infinity" an accepted terminology ? :yuck:Hurkyl said:

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.

I would have used different words !

- #5

- 13,017

- 566

Gokul43201 said:So, is "almost infinity" an accepted terminology ? :yuck:

I would have used different words !

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.

- #6

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

- #7

Gokul43201

Staff Emeritus

Science Advisor

Gold Member

- 7,051

- 18

Gotcha ! It's an inside thing.Hurkyl said:Of course, I would never say things in such a way except around people where there was no chance of misunderstanding.

- #8

SGT

- #9

Icebreaker

Maybe he was talking about infinite sets.

- #10

- 138

- 0

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.vikasj007 said:

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.

- #11

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

Mathematically, we like to use definitions somewhat more precise than that. :tongue2:Infinity by definition is no end or no limit

- #12

- 609

- 0

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...

- #13

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

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

- #14

- 37

- 0

Healey01 said: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)

- #15

- 161

- 0

- #16

- 609

- 0

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.vikasj007 said:

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.

- #17

Icebreaker

There's infinite sets.

- Last Post

- Replies
- 24

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 18

- Views
- 3K

- Last Post

- Replies
- 22

- Views
- 4K

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 12

- Views
- 2K

- Last Post

- Replies
- 38

- Views
- 5K

- Last Post

- Replies
- 18

- Views
- 3K

- Last Post

- Replies
- 16

- Views
- 3K

- Last Post

- Replies
- 11

- Views
- 1K