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R H Draney turpitued:

Only if your head is spinning.

Peter Moylan peter at ee dot newcastle dot edu dot au http://eepjm.newcastle.edu.au (OS/2 and eCS information and software)

dcw filted:

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

or any multiple thereof..r

Only if your head is spinning.

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:

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)

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.

NB mail to my.spamtrap (at) verizon.net is heavily filtered to remove spam. If your message looks like spam I may not see it.

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.

NB mail to my.spamtrap (at) verizon.net is heavily filtered to remove spam. If your message looks like spam I may not see it.

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:

What's the angular diameter of a watchspring when you're in the middle of it?...r

R H Draney turpitued:

dcw filted: or any multiple thereof..r

Only if your head is spinning.

What's the angular diameter of a watchspring when you're in the middle of it?...r

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