# re: "Finite" For "Greater Than Zero"page 6

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R H Draney turpitued:
dcw filted:

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

or any multiple thereof..r

Peter Moylan peter at ee dot newcastle dot edu dot au http://eepjm.newcastle.edu.au (OS/2 and eCS information and software)
Bob Cunningham turpitued:
A response that seemed to be coming from a qualified scientist held that "exponential growth" is commonly understood to mean explosively rapid growth even among physicists who really know better.

The physicists are the ones who don't call it a quantum leap.

Peter Moylan peter at ee dot newcastle dot edu dot au http://eepjm.newcastle.edu.au (OS/2 and eCS information and software)
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Nought point three recurring is not a finite number.

Chop off a finger, and it becomes 0.3 exactly. There's nothing especially priviledged about base 10.
But that's not what "infinite" means. "Infinite" isn't "can't be represented in a finite decimal expansion" or even "can't be represented by a finite-length description"(1). It's (roughly) "greater (or less) than every integer". 1/3 is less than one. It's finite.
(1) Of which "naught point three recurring" is a fine example. As is "1/3" or "the probability of throwing a number smaller than three on a regular six-sided die". There are more finite numbers that don't have a finite-length description in, say, English, than that do. Infinitely more.

Evan Kirshenbaum + HP Laboratories >We never met anyone who believed in
1501 Page Mill Road, 1U, MS 1141 >fortune cookies. That's astounding.Palo Alto, CA 94304 >Belief in the precognitive powers
I started that thread, in 2003 I think. See the entry titled exponential growth at wikipedia.org . Mike Hardy

I thought maybe he was thinking about the time I objected to "exponential growth" meaning "get big fast" on 10 October
1997 under the subject line "Exponential vs Geometric".

In that same thread I also objected to "finite" being used to mean "non-zero".
Nought point three recurring is not a finite number.

In addition to Evan's comments, the probability you seek is not
0.333..., it's 1/3, which is an exact representation.
dg (domain=ccwebster)
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We are in danger of drifting into maths again. Note that "infinitessimal" is not part of standard (*) maths.

Really? In high school calculus for me, quantities approaching zero in the limit were called "infinitesimal" (and "infinitesimals"). I've always assumed that it was standard terminology.

By using the 19th-century definitions of limit that you used (epsilon-delta arguments and all that), those quantities at any given time took only finite (non-infinitesimal) values, so that you never had to really deal with infinitesimal quantities as such. It is of course conventional, for historical reasons, to talk about, for example, the derivative as a ratio infinitesimals and the integral as a sum of infinitesimals. The 17th- and 18th-century mathematicians who invented calculus and analysis didn't care about such methodological niceties (or at least most of them didn't), and in any event they couldn't see a way around talking about infinitesimals, so they just plunged ahead in their own non-rigorous, bravura way, sidestepping the occasional paradoxes or contradictions they along the way encountered as best they could.
The branch of mathematics that treats those infinitesimals as actual infinitesimal (but non-zero) numbers in a rigorous way, which was developed only in the second half of the 20th century, is called "non-standard analysis". "Standard" mathematics (in this context, at least) is everything else.

Roland Hutchinson              Will play viola da gamba for food.

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I think it arose because people perceived a need for ... for the original example "non-zero" would have done as well.

But in that use, 'finite' covers both ends of the spectrum: non-zero and not infinite. It's an economical way of saying that it's a number you could make definite if you had to, which you couldn't if it were indefinitely large or small.

But it doesn't really mean non-zero. It means non-infinitesimal. They aren't quite the same thing. (It happens that in talking about the angular diameter of the sun in the context given, the difference between an infinitesimal and a zero diameter is unimportant, but its not true in general that the distinction between infinitesimal and zero can be ignored.)

Roland Hutchinson              Will play viola da gamba for food.

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I started that thread, in 2003 I think. See the entry titled exponential growth at wikipedia.org . Mike Hardy

I thought maybe he was thinking about the time I objected to "exponential growth" meaning "get big fast" on 10 October
1997 under the subject line "Exponential vs Geometric".

In that same thread I also objected to "finite" being used to mean "non-zero".
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Peter Moylan filted:
R H Draney turpitued:

dcw filted: or any multiple thereof..r