# Is 0 a finite number?

TitusvE
Science 20 Aug '10 12:52
1. 20 Aug '10 12:521 edit
I would say yes. However, scientist often use terminology such as "finite temperature" meaning a temperature larger than 0 K. I always tried to refrain from using such sentence because I thought it was an incorrect use of words. In the beginning I even got annoyed that scientist, especially the ones working in the field of physics or mathematics ( "the exact sciences" ), are so sloppy with definitions. I assumed that someone started to use "finite" is this wrong manner and that others just started to copy this behavior without thinking for themselves realizing the true meaning of the word "finite". However, now I start to doubt. ..
Wikipedia (en.wikipedia.org/wiki/Finite) and some online dictionaries e.g (http://dictionary.reference.com/browse/finite) have adopted the option "finite =/ 0" as a possible definition. Is this just because some faults get accepted when many people make them? Or is "finite" as being nonzero actually truly correct?
2. 20 Aug '10 16:52
It depends on the context, and usually it will be clear from the context what kind of definition of "finite" is used. Generally, if you are regarding a variable which can be infinite, then finite can also include zero. If you regard a variable which is never infinite, then "finite" usually means a nonzero number.
3. 20 Aug '10 18:28
Yes, I know how to interprete the word "finite" in a certain context. I understand that sometimes people mean nonzero when saying "finite". This doesnot mean it is a correct way of saying.
4. 20 Aug '10 18:42
Originally posted by TitusvE
Yes, I know how to interprete the word "finite" in a certain context. I understand that sometimes people mean nonzero when saying "finite". This doesnot mean it is a correct way of saying.
Well, that's all semantics, isn't it?
5. 20 Aug '10 18:46
Originally posted by TitusvE
Yes, I know how to interprete the word "finite" in a certain context. I understand that sometimes people mean nonzero when saying "finite". This doesnot mean it is a correct way of saying.
With language, there are dictionary definitions, there is general usage, there is exceptional usage, there is poor usage, and even incorrect usage.
But 'correct usage' is not such clearly defined area. If enough people are using the word in a given way then that is correct usage.
6. AThousandYoung
West Coast Rioter
20 Aug '10 19:27
Originally posted by TitusvE
However, scientist often use terminology such as "finite temperature" meaning a temperature larger than 0 K.
Which scientists are these?
7. 20 Aug '10 20:07
Originally posted by AThousandYoung
Which scientists are these?
Ultracold physicists tend to since models tend to be different for zero or finite temperature.
8. AThousandYoung
West Coast Rioter
21 Aug '10 00:50
Originally posted by KazetNagorra
Ultracold physicists tend to since models tend to be different for zero or finite temperature.
Well that's silly.
9. 21 Aug '10 06:25
Also statistical physicists. A T=0 K calculation will refer to finding the absolute minimum in a potential energy landscape while "finite temperature" calculation refers to a Monte-Carlo or Molecular-Dynamics calculation where the whole space is sampled according to its Boltzmann weight exp(-beta V) with beta =1/(kB T). Finite "beta" would actually be correct way of saying
10. 21 Aug '10 06:471 edit
Originally posted by KazetNagorra
Well, that's all semantics, isn't it?

What do you mean by that? That we should not bother as long as things are clear what people mean by it? Shouldn't scientist be a bit more careful with their words and definitions than the man in the street? Suppose we are messing with other defitions and make their meaning dependent on the context. Soon different scientific fields can no longer talk to each other.

On the other hand I read somewhere that finite (the inverse of infinite) could also be viewed as the inverse of infinitesimal when meaning nonzero. But what is language-speaking the correct inverse infinitesimal? finitesimal??

But do you agree that using "finite" for nonzero is wrong, in principle?
11. 21 Aug '10 08:32
Originally posted by TitusvE
Originally posted by KazetNagorra
[b]Well, that's all semantics, isn't it?

What do you mean by that? That we should not bother as long as things are clear what people mean by it? Shouldn't scientist be a bit more careful with their words and definitions than the man in the street? Suppose we are messing with other defitions and make their me ...[text shortened]... ? finitesimal??

But do you agree that using "finite" for nonzero is wrong, in principle?[/b]
I agree pretty much with what twhitehead says.
12. sonhouse
Fast and Curious
21 Aug '10 15:08
Originally posted by KazetNagorra
Ultracold physicists tend to since models tend to be different for zero or finite temperature.
If I have it correct, absolute zero is not neccesarily an asymtote limit. The way we are pursuing it now seems that way but absolute zero temperature is not the same as absolute zero energy. It may well be in some future experiment absolute zero temperature is reached, it just means absolute stillness. Heisenberg saw to that. So in my mind absolute zero is not unreachable and therefore is finite.
13. 21 Aug '10 15:13
Originally posted by TitusvE
But do you agree that using "finite" for nonzero is wrong, in principle?
Let us instead try the word "measurable" in place of "finite". In some contexts, infinitely large distances are not measurable but a zero distance is. In other contexts, it is the infinitely small distances that are not measurable.
A zero temperate is not really meaningful, all we really have is very very low temperatures, and the infinitely small ones are not measurable.
So if by 'finite' you mean 'it can be given an exact measure' then it works in both contexts.

Also if you think about it in terms of set theory. Zero is a number on the number line and is a member of many finite sets, but is the empty set a finite set?
14. 09 Sep '10 10:02
Mathematically it's finite.

Physical sciences-wise, not really. Though zero is certainly more finite than the singular extremums of GR.
15. 12 Sep '10 00:50
Last time I heard, we could never reach absolute zero. It seems that this is more of an issue of being able to reach absolute zero than the number zero.