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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Newsgroups | sci.math |
| Subject | Re: Question about unbounded infinite sets... |
| Date | 2024-02-16 21:07 +0000 |
| Organization | A noiseless patient Spider |
| Message-ID | <87bk8gjey1.fsf@bsb.me.uk> (permalink) |
| References | <uqohpe$11fn$1@dont-email.me> |
"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
> Take a number that wants to get close to zero.
This makes no sense. "a number" is one number. And numbers don't want
anything.
> Say:
>
> [0] = 1
> [1] = .1
> [2] = .01
> [3] = .001
> [...] = [...]
Strange notation. [0] = 1. Eh? Why not just use a more conventional
notation for a s sequence:
s_0 = 1
s_1 = 0.1
etc.
You can, if you prefer, write it as a function: s(n) = 10^-n (as you do
later).
> This gets close to zero, yet never will equal zero. Okay so:
>
> arbitrarily close seems to be the accepted term.
But it's not a very good one. For example, one could say that
p(n) = 2^n when n is even
p(n) = 2^-n when n is odd
gets arbitrarily close to zero but also arbitrarily far away from zero.
> infinitely close is the wrong wording?
I would not know what you mean if you said that, so I would say it's the
wrong wording. The best wording is to say
lim_{n->oo} s(n) = 0.
which you can read as "the limit, as n tends to infinity, if s(n) is
zero".
> The function f(n) = 10^(-n) gets "infinitely close" to 0... lol. Using the
> "metaphysical formation" of arbitrarily close... ;^)
Oh. Does the ;^) mean this as all a joke? If so, sorry.
--
Ben.
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Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-16 12:49 -0800
Re: Question about unbounded infinite sets... Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-16 21:07 +0000
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Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-22 12:04 +0000
Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-22 07:17 -0500
Re: Question about unbounded infinite sets... WM <wolfgang.mueckenheim@tha.de> - 2024-02-22 14:11 +0000
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Re: Question about unbounded infinite sets... Richard Damon <richard@damon-family.org> - 2024-02-18 07:36 -0500
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Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-16 15:12 -0800
Re: Question about unbounded infinite sets... FromTheRafters <FTR@nomail.afraid.org> - 2024-02-16 17:33 -0500
Re: Question about unbounded infinite sets... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-16 15:16 -0800
Re: Question about unbounded infinite sets... FromTheRafters <FTR@nomail.afraid.org> - 2024-02-17 06:33 -0500
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