# "Finite" For "Greater Than Zero"

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I was just thinking about this the other day, and since a good example drifted by on another ng, I thought I'd bring it up.

I sometimes see "finite" used where a meaning of "greater than zero" seems intended, rather than one of "not infinite". An example came up in a discussion of life near the Arctic Circle: "since the sun has a finite angular diameter, the night and day durations are asymmetric". I think I've also heard similar usages from mathematicians. Comments?
Aaron Davies
Opinions expressed are solely those of a random number generator. "I don't know if it's real or not but it is a myth." -Jami JoAnne of alt.folklore.urban, showing her grasp on reality.
Aaron Davies filted:
I was just thinking about this the other day, and since a good example drifted by on another ng, I ... finite angular diameter, the night and day durations are asymmetric". I think I've also heard similar usages from mathematicians. Comments?

It's a shorthand way of saying "not infinitesimally small", and a shorthand that's become widespread enough to be useful...saves no fewer than seven syllables, so what the heck..r
I was just thinking about this the other day, and since a good example drifted by on another ng, I ... finite angular diameter, the night and day durations are asymmetric". I think I've also heard similar usages from mathematicians. Comments?

Yes, I can't grasp the point of your question. Surely "infinite" itself was based on "not finite," so there's no real problem in saying that "finite" means "not infinite". Another pair: Impossible = not possible. Possible = not impossible.
M-W offers several nice definitions of "finite" aren't they appropriate for your "angular diameter" example? It sounds like the "definite, measurable" one to me.
For you to bring in "greater than zero" suggests that negative numbers are ruled out, but for many sorts of measurements, they were never ruled *in*.
I don't know what an angular diameter means, really, but a diameter is always a length, as far as I know, and can't be less than zero. Angle measurement in certain circumstances can be negative, to convey direction of motion, but does that make sense here?

I wonder if a different example would make the case better.
Best Donna Richoux
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Yes, I can't grasp the point of your question. Surely "infinite" itself was based on "not finite," so there's no real problem in saying that "finite" means "not infinite". Another pair: Impossible = not possible. Possible = not impossible.

Yes; that's the common meaning with which I'm contrasting this "new" meaning.
M-W offers several nice definitions of "finite" aren't they appropriate for your "angular diameter" example? It sounds like the ... than zero" suggests that negative numbers are ruled out, but for many sorts of measurements, they were never ruled *in*.

OK, non-zero then.
I don't know what an angular diameter means, really, but a diameter is always a length, as far as I ... zero. Angle measurement in certain circumstances can be negative, to convey direction of motion, but does that make sense here?

Angular diameter is the angle subtended by the diameter of an object when viewed; I think the sun is about half a degree.
I wonder if a different example would make the case better.

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.

Aaron Davies
Opinions expressed are solely those of a random number generator. "I don't know if it's real or not but it is a myth." -Jami JoAnne of alt.folklore.urban, showing her grasp on reality.

Yes, I can't grasp the point of your question. Surely "infinite" itself was based on "not finite," so there's no ... zero. Angle measurement in certain circumstances can be negative, to convey direction of motion, but does that make sense here?

The angular diameter is the angle subtended by the apparent diameter of the sun. The angle would be between the lines traced from, say, the top-most point of the sun, to your eye, to the bottom-most point of the sun. Interestingly, the angular diameter of the sun is very close to that of the moon, though they are vastly different in actual size.

Incidentally, the quoted passage is drivel. The angular diameter of the sun has nothing to do with the relative lengths of night and day in the arctic. It is approximately the same for all observers on earth. The durations of days are due to the earth's tilt relative to its axis of rotation about the sun.
Don
Kansas City

Yes, I can't grasp the point of your question. Surely "infinite" itself was based on "not finite," so there's no real problem in saying that "finite" means "not infinite".

...
In this case though, the meaning seems to be "not infinitesimal" or "not immeasurably or incalculably small". Does "finite" cover this condition in addition to its usual meaning?

dg (domain=ccwebster)
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In this case though, the meaning seems to be "not infinitesimal" or "not immeasurably or incalculably small". Does "finite" cover this condition in addition to its usual meaning?

Now that's an excellent question. As an engineer who uses a lot of math, my opinion would be that it should (though, maybe it doesn't literally) also mean "not infinitesimal".
When I read "finite", I interpret it to mean "of a definite, measurable value". Oh hell; now we have *de*-finite!
Don
Kansas City
In this case though, the meaning seems to be "not ... "finite" cover this condition in addition to its usual meaning?

Now that's an excellent question. As an engineer who uses a lot of math, my opinion would be that it ... When I read "finite", I interpret it to mean "of a definite, measurable value". Oh hell; now we have *de*-finite!

I'm cool with "finite" implying a "measurable quantity or value".
dg (domain=ccwebster)
Aaron Davies:
I sometimes see "finite" used where a meaning of "greater ... I think I've also heard similar usages from mathematicians. Comments?

I find it bothersome but convenient.
Donna Richoux:
Yes, I can't grasp the point of your question. Surely "infinite" itself was based on "not finite," so there's no real problem in saying that "finite" means "not infinite". ...

Well, exactly. But in this usage the meaning isn't "not infinite"; it's "greater than zero" or "not zero".
For you to bring in "greater than zero" suggests that negative numbers are ruled out, but for many sorts of measurements, they were never ruled *in*.

Indeed, I think this usage only occurs in contexts where the value in question must be either zero or a (finite) positive number. Which means (1) that "greater than zero" and "not zero" are effectively equivalent in the context, and (2) that an actual infinity is imposssble, so there is no real ambiguity. You could think of "finite" in this sense as meaning "neither zero nor infinite", if you like.
I don't know what an angular diameter means, really, but a diameter is always a length, as far as I know, and can't be less than zero.

But it can be equal to zero, and this usage of "finite" means that it's not.
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