Even before you get to limits, I think you have to establish whether they can parse the phrase "two different ways of writing the same number". Some cannot. On November 14, 2012 at 2:07 AM Dan Asimov <dasimov@earthlink.net> wrote:> Mike, I could not tell you what "those same people" think.
But maybe by asking the questions you're asking, more of them could be persuaded to see the error of their ways.
(To start with, virtually none of them seem to know or care about the rigorous definition of limit.)
--Dan
On 2012-11-13, at 10:11 PM, Mike Speciner wrote:
Do those same people think that 0.3333... doesn't equal 1/3? And if 0.3333... isn't 1/3, then how do you represent 1/3 in decimal? And if it does equal 1/3, doesn't multiplying by 3 give 0.9999... ?
On 2012-11-14 00:32, Dan Asimov wrote:
I'm pretty sure the shift in thinking -- at least among mathematicians -- occurred when Cauchy came up with the modern epsilon-delta definition of limit. Which Wikipedia says occurred in 1821.
I've seen way too many non-mathematically trained people insisting (e.g., on sci.math) that 0.9999... definitely does not, can not, equal 1. So I guess the shift among non-mathematicians is still in progress.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun