# re: "Finite" For "Greater Than Zero"page 3

•  197
Aaron Davies turpitued:
I've heard people talk about "finite" probabilities before, when what they mean is that the probability of a given event is greater than zero i.e., that it can in fact happen.

Careful! "With probability zero" does not mean the same as "can never happen".

Peter Moylan peter at ee dot newcastle dot edu dot au http://eepjm.newcastle.edu.au (OS/2 and eCS information and software)
Aaron Davies filted:
Pragmatics. The obvious intent is to contrast the Sun with a point source i.e., one of zero angular diameter. Furthermore, there's no such thing as infinite angular diameter.

Your last sentence and Mark Brader's make essentially the same claim...but tell me, couldn't you say an object had an infinite angular diameter if you were, say, inside it?...r
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But probabilities are represented by a number between zero and ... are greater than zero and are either finite or not.

I find it hard to get a handle on an infinite probability.

You and me both, man. However, in the archives are very, very, very long discussions about whether such a notion has ever been properly defined (and its companion notion, selecting an item "at random" from an infinite set). It would probably be a kindness to the group not to go down that path again.
Even if we happen to have some members itching to set us all straight.

...but tell me, couldn't you say an object had an infinite angular diameter if you were, say, inside it?...r

No; it would have an angular diameter of 2 pi, or 360 degrees.

David
I was just thinking about this the other day, and since a goodexample drifted by on another ng, I thought ... know if it's real or not but it is a myth." -Jami JoAnne of alt.folklore.urban, showing her grasp on reality.

This odd usage has been around for quite some time. In most branches of maths, at least, it would be regarded as wrong: zero is finite. But, as discussed in another recent maths thread, mathematical terms are not subject to ISO standards or anything like that and do vary from branch to branch and author to author. I do not personally know a branch of maths in which zero is not regarded as finite but I would not rule out the existence of one. If I read some maths on a topic that I am unfamiliar with, I need to avoid assuming that familiar terms have the familiar meanings.
So, there is a chance that the usage has leaked out of some odd branch of maths. Another possibility is that it is just nonsense. If you search the group for older maths threads, you will find one about exponential growth. It is popularly used in ways that I am sure are not correct in any branch of maths.
If you hear "finite" from a non-mathematician, you need to ask or judge from the context what he really means. If you hear it from a mathematician, you may be able to calculate the meaning based on the subject area or references that he has made previously.

Se=E1n O'Leathl=F3bhair
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I think it arose because people perceived a need for a word for "not infinitesimal". It was perhaps a bad choice, and for the original example "non-zero" would have done as well.
Katy
You and me both, man. However, in the archives are very, very, verylong discussions about whether such a notion has ... Even if we happen to have some members itching to set us allstraight. Sadder but wiser Donna Richoux

No itch here. I can resist talking about probability easily.

Se=E1n O'Leathl=F3bhair
dcw filted:
...but tell me, couldn't you say an object had an infinite angular diameter if you were, say, inside it?...r

No; it would have an angular diameter of 2 pi, or 360 degrees.

or any multiple thereof..r
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But probabilities are represented by a number between zero and ... are greater than zero and are either finite or not.

I find it hard to get a handle on an infinite probability. The range is only from 'not ever' (zero) to 'certainly' (one). Infinite improbability, though, just needs a cup of tea, Brownian motion, and a shipboard computer named Eddie (for the currents, I suppose).

And the probability of throwing a number smaller than three on a regular six-sided die?

John Dean
Oxford