Re: limitation to induction on finite bounds
From: Peter R. Douglass (peterd_at_ccs.neu.edu)
Date: 07/13/04
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Date: Tue, 13 Jul 2004 11:19:25 -0400
responding to "|-|erc" <gotch@beauty.com>
message news:iXRIc.92636$sj4.53983@news-server.bigpond.net.au...
HERC > Can you find a number of sequential 3's not present in
HERC > {0.1, 0.2, 0.3, ...0.29, 0.31, 0.32, 0.33, 0.34, ... 0.332,
HERC > 0.333, ...} ?
PRD > I do not know what it means to be "not present". Does that
PRD > mean "not occur" or does that mean "not an element" or
PRD > does that mean something else?
HERC > this string has 5 sequential 3's present 010101055555010101
HERC > this set has 6 sequential 3's present
HERC > {0, 222, 33, 999, 333333, 222, 888}
HERC > this set has 7 sequential 3's present
HERC > {1, 222, 333, 8883333333999, 33333033333, 888}
HERC > Is that clear enough to tackle this question?
No. On 2004-07-05 I wrote
PRD > It would seem by your answers that a statement
PRD > "x occurs in the set 010203" means something
PRD > different than "x is an element of the set 010203"
The same day you responded to that question
HERC > yes.
HERC > as the set approaches infinite length, the element occurs
In the examples you
give, 33333 occurs in the first set, and it is also an element of
the first set. Similarly for the other examples. So please answer
the question. Does "not present" mean the same as "not occur",
"not an element" or something else?
HERC > Can you find a number of sequential 3's not present in
HERC > {0.1, 0.2, 0.3, ...0.29, 0.31, 0.32, 0.33, 0.34, ... 0.332,
HERC > 0.333, ...} ?
I do not know what "find" means. Are you asking whether
there is a sequence of threes which does not occur? Whether
there is a sequence of threes which is not an element? Are
you asking something else?
HERC > Originally you asked for this form.
HERC > XXXX -> does not occur.
HERC > Then you utilised it for a DEFINITION.
PRD > Please post a quote illustrating what you mean[t] by this.
HERC > Its scrolled off my newsreader. This is Occur defn from 7/9/04
You can find all of the posts on google
HERC > d occurs in S
HERC > <->
HERC > An e N , if (finite(length(d)), n<= length(d)) (i.e. regardless if
its infinite or finite)
HERC > Ei,
HERC > digitsmatchupton(i, d, n)
But I did not write this, you did.
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