# re: "Finite" For "Greater Than Zero"page 2

•  197
Aaron Davies:

Don Gilmore:
Incidentally, the quoted passage is drivel.

No, it isn't.
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.

Yes, which is why the day and night durations are asymmetric for all observers on Earth. It's just that in the polar regions, this effect is more noticeable because sunrise and sunset are so much slower.

Actually, this depends on exactly how "day" and "night" are being defined. If you define them in terms of the center of the Sun crossing the horizon (and ignore effects of atmospheric refraction, not mentioned in the quoted passage), then there is no asymmetry. But a more practical definition would be that night is when the Sun is fully below the horizon, i.e. from last contact of sunset until first contact of sunrise; then night is, on average, shorter than day, for the reason stated, and atmospheric refraction further increases the difference.
The durations of days are due to the earth's tilt relative to its axis of rotation about the sun.

Primarily, yes. (There are second-order effects due to the Earth's orbit not being circular.)

Mark Brader "One might as well complain about the Sun Toronto rising in the daytime instead of at night, (Email Removed) when we need it more." John Lawler

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?

I think some mangling of terms is at work. Mathematicians won't mistakenly speak of zero as if it is not finite or could somehow impliedly not be finite, nor forget that hordes of negative numbers are finite, though perhaps people applying mathematics to something might mangle the concepts.I do hear scientists applying mathematics, not mathematicians, speak of a "finite" difference from zero to indicate nonzero value of something that converges on some nonzero value as an extreme case is reached. This is a poor use actually. Something infinitesimally greater than zero is never zero and cannot be 1 or larger than 1, it is a bound expression and prevented from being infinite on the real number line even though we cannot say exactly what number value it corresponds to while it is indefinite.

But the durn thing is already "finite", potentially, even in its indefinite form, and if it turns out to be zero when transformed into a definite expression it is still "finite"! Once we evaluate an infinitesimal we have arrived at a (potentially) definite value and to express that it is a definite value greater than zero we only need call it a "positive" value, thus the conventional proper phrases most scientists are looking for: "positive definite value" or "positive value" (if still variable but never zero) or even simply "nonzero value".
I also hear scientists speak of a "finite" result to indicate that a realistic quantity demonstrating actual existence rather than an abstract or theoretical existence. Really the better term would seem to be "reasonable" or "realistic" or "affirmative" rather than "finite" as a quantity. A lot of scientist may be mangling the term "finite", but I doubt mathematicians are.
The common mathematical phrase for a definite value greater than zero is "positive definite value". More scientists should listen to the language of mathematicians rather than play games with the terms. Zero is a finite value, but never a positive one, and a positive value is never zero. If it is a variable value that is always positive, never zero, "positive value" is all one need say.
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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?

I don't see why you think "finite" here means "greater than zero". It's certainly true that the Sun's A.D. *is* greater than zero but it's also true that it is not infinite. So why plump for the unusual meaning? I see no evidence for it.

John Dean
Oxford
Now that's an excellent question. As an engineer who uses ... a definite, measurable value". Oh hell; now we have *de*-finite!

I'm cool with "finite" implying a "measurable quantity or value".

I'll rephrase that to "measurable quantity or calculable value". That includes zero, by the way.

dg (domain=ccwebster)
But probabilities are represented by a number between zero and one inclusive. A probability of zero is finite but it would, I think, be unusual to emphasise the fact. All other probabilities are greater than zero and are either finite or not.

John Dean
Oxford
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Aaron Davies:
I sometimes see "finite" used where a meaning of "greater ... I think I've also heard similar usages from mathematicians. Comments?

John Dean:
I don't see why you think "finite" here means "greater than zero". It's certainly true that the Sun's A.D. *is* greater than zero but it's also true that it is not infinite. So why plump for the unusual meaning?

Because it's the fact that the angular diameter is nonzero that makes the durations of day and night asymmetric, whereas the angular diameter of an object cannot possibly be infinite.

Mark Brader > "I do not want to give the impression I spend all Toronto > my time on the Internet, but in the right hands (Email Removed) > it is a wondrous tool, and in the wrong hands
I've heard people talk about "finite" probabilities before, when what ... is greater than zero i.e., that it can in fact happen.

But probabilities are represented by a number between zero and one inclusive. A probability of zero is finite but it would, I think, be unusual to emphasise the fact. All other probabilities 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).
Paul
In bocca al Lupo!

I don't see why you think "finite" here means "greater than zero". It's certainly true that the Sun's A.D. *is* greater than zero but it's also true that it is not infinite. So why plump for the unusual meaning? I see no evidence for it.

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.

Aaron Davies
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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?

A mathematician would say "positive" (or "strictly positive" to eliminate possible ambiguity).

J.