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From M-W:...In reply to:LIMIT: 6 a : a number whose numerical difference from a mathematical function is arbitrarily small for all values of the independent variables that are sufficiently close to but not equal to given prescribed numbers or that are sufficiently large positively or negatively b : a number that for an infinite sequence of numbers is such that ultimately each of the remaining terms of the sequence differs from this number by less than any given positive amount
The above definition explains why I think that 2.9999... illustrates the concept of a limit of 3. The limit is 3, but as x approaches the limit it becomes infinitely close to 3 without quite becoming three. Sounds like 2.99999... to me.
Bean wrote:In reply to:Making up an entirely different function from the one being discussed that shows that the limit OF THE PARTICULAR FUNCTION is different when approaching from above or below has no relevance to this argument, which is "how do we write the number 3?", not "can we think of a function that has a limit that is undefined at 3?". Certainly f(x) = 3/(x-3) is undefined at x = 3 but that doesn't tell you a lot about the point x = 3 on the number line..
Yes but my point has to do with those two values that are not quite three. The function serves to illustrate the difference between 2.999999... and (4-0.99999...). The point at which x=3 itself has no bearing whatsoever on my argument.
Of course the big problem here is that I seem to be picking one nit and you seem to be picking another.
Entire Thread Subject Posted By Posted dr rav 01/21/03 05:27 PM Re: dr wentworth 01/21/03 05:36 PM Re: dr Faldage 01/21/03 05:42 PM Re: dr Wordwind 01/21/03 06:04 PM Re: dr wwh 01/21/03 06:17 PM Re: Dr or Dr. wwh 01/21/03 06:20 PM Re: dr Faldage 01/21/03 06:33 PM Re: dr wwh 01/21/03 06:54 PM Re: dr Faldage 01/21/03 07:23 PM Re: dr wwh 01/21/03 07:43 PM Re: dr AnnaStrophic 01/21/03 11:25 PM Re: dr rav 01/22/03 01:55 PM Re: dr TheFallibleFiend 01/21/03 09:43 PM Re: dr johnjohn 01/21/03 11:25 PM Re: dr wwh 01/22/03 01:34 AM Re: dr Faldage 01/22/03 11:05 AM The RhubarbCommando speaks out for Britain. RhubarbCommando 01/22/03 12:24 PM Re: dr boronia 01/22/03 02:03 PM Post deleted by Wordwind Wordwind 01/22/03 02:10 PM Re: dr rkay 01/23/03 09:19 AM Re: dr Capfka 01/23/03 11:19 AM Re: dr Bean 01/22/03 02:55 PM Re: dr TheFallibleFiend 01/22/03 03:14 PM Re: dr Bean 01/22/03 04:05 PM Re: dr TheFallibleFiend 01/22/03 07:02 PM Re: dr Faldage 01/22/03 07:32 PM Re: dr TheFallibleFiend 01/22/03 08:23 PM Re: dr Faldage 01/22/03 08:29 PM Re: dr Bean 01/23/03 11:34 AM math emanuela 01/28/03 04:54 PM answer emanuela 01/28/03 04:55 PM Re: answer Faldage 01/28/03 06:38 PM Re: answer wwh 01/28/03 06:46 PM Re: answer Faldage 01/28/03 07:08 PM Re: answer wwh 01/28/03 07:45 PM Re: answer Faldage 01/28/03 07:53 PM Re: answer Alex Williams 01/28/03 10:38 PM Re: answer Bean 01/28/03 11:46 PM Re: answer tsuwm 01/29/03 12:11 AM Post deleted by Wordwind Wordwind 01/29/03 12:16 AM e Alex Williams 01/29/03 02:04 AM Re: e Faldage 01/29/03 11:05 AM Re: e Bean 01/29/03 11:10 AM Re: e Bean 01/29/03 11:14 AM Re: e TheFallibleFiend 01/29/03 11:50 AM Re: e Alex Williams 01/29/03 01:48 PM Re: e TheFallibleFiend 01/29/03 02:10 PM Re: e Faldage 01/29/03 02:36 PM Re: e Bean 01/29/03 02:49 PM Re: one = non-one tsuwm 01/29/03 02:58 PM Re: one = non-one Bean 01/29/03 03:12 PM Re: e Faldage 01/29/03 03:16 PM Re: e Bean 01/29/03 03:54 PM Re: e Alex Williams 01/29/03 04:13 PM Re: e tsuwm 01/29/03 04:18 PM Re: e Faldage 01/29/03 04:33 PM Re: e Alex Williams 01/29/03 05:04 PM Re: e Buffalo Shrdlu 01/29/03 05:32 PM Re: e Alex Williams 01/29/03 06:04 PM Re: e Faldage 01/29/03 06:06 PM infinity emanuela 01/30/03 06:36 AM Re: infinity Alex Williams 01/30/03 10:40 AM Re: infinity Bean 01/30/03 11:24 AM Re: numbers real and rational Faldage 01/30/03 12:03 PM Re: numbers real and rational Alex Williams 01/30/03 01:01 PM Re: numbers real and rational emanuela 01/30/03 01:56 PM Re: numbers real and rational Faldage 01/30/03 02:00 PM . Alex Williams 01/30/03 03:22 PM Re: . Faldage 01/30/03 03:31 PM Re: e Bean 01/29/03 04:32 PM Re: e Bean 01/29/03 02:45 PM math is not an exact science wofahulicodoc 01/30/03 03:31 PM numbers emanuela 01/30/03 04:54 PM Re: math Faldage 01/28/03 05:15 PM Re: math wwh 01/28/03 06:00 PM Re: math musick 01/28/03 06:16 PM parallel lines emanuela 01/29/03 01:31 PM 0,99999..... emanuela 01/29/03 01:17 PM Re: dr vika 01/28/03 04:42 PM Re: dr rav 01/22/03 08:51 PM Re: dr modestgoddess 01/23/03 08:32 PM Re: dr Faldage 01/23/03 08:40 PM Re: dr modestgoddess 01/23/03 08:44 PM Re: dr Bean 01/24/03 12:09 AM Re: dr Capfka 01/24/03 08:46 PM Re: dr Faldage 01/27/03 07:56 PM Re: dr AnnaStrophic 01/27/03 07:58 PM Re: duhing … and three dots Faldage 01/27/03 08:08 PM Re: duhing … and three dots wwh 01/27/03 08:15 PM Re: duhing … and three dots Faldage 01/27/03 08:18 PM Re: dr tsuwm 01/27/03 08:04 PM
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