David Kastrup wrote:> quasi <quasi@null.set> writes: > > >>On 25 Jul 2005 23:22:08 GMT, rusin@vesuvius.math.niu.edu (Dave Rusin) >>wrote: >> >> >>>The intuition with limits may >>>be important in some contexts but there is a priori nothing wrong >>>with a definition like >>> >>>1. x^0 =1 if x > 0. >>>2. 0^x = 0 if x > 0. >>>3. 0^0 = 17 >> >>Sure the definition of 0^0 is arbitrary but the only natural choices >>are "undefined", 0, or 1. As for 0 or 1, even disregarding the >>continuity argument, why should 0^x have priority over x^0 or vice >>versa. > > > Because 0^x is discontinous at 0 even if you set 0^x=0? Setting it at > 0 only for one-sided continuity seems to be less useful than setting > it to 1 for total continuity of x^0 everywhere on C.Have we looked at exp(-1/x) lately? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
collection of mathematically elegant tricks
Started by ●July 24, 2005
Reply by ●July 26, 20052005-07-26
Reply by ●July 26, 20052005-07-26
On Tue, 26 Jul 2005 00:16:51 -0700, quasi <quasi@null.set> wrote:>On 25 Jul 2005 23:22:08 GMT, rusin@vesuvius.math.niu.edu (Dave Rusin) >wrote: > >>The intuition with limits may >>be important in some contexts but there is a priori nothing wrong >>with a definition like >> >> 1. x^0 =1 if x > 0. >> 2. 0^x = 0 if x > 0. >> 3. 0^0 = 17 > >Sure the definition of 0^0 is arbitrary but the only natural choices >are "undefined", 0, or 1. As for 0 or 1, even disregarding the >continuity argument, why should 0^x have priority over x^0 or vice >versa.What is unnatural about: For any a>1 (a^(-1/x)) ^ x = 1/a if x>0?
Reply by ●July 26, 20052005-07-26
"ToddSmith" <elliptic1@gmail.com> wrote in message news:1122342726.367323.304240@f14g2000cwb.googlegroups.com...> Yes the code you use to write equations is basically the same as TeX. > Thanks for going to it. Post some stuff! > > -Todd Smith > www.exampleproblems.com >Hi Todd, When I went to the forum session, http://www.exampleproblems.com/phpbb/ The equation editing feature was gone. So the forum itself does not support Latex equations, right? Thanks a lot!
Reply by ●July 27, 20052005-07-27
"ToddSmith" <elliptic1@gmail.com> wrote in message news:1122342726.367323.304240@f14g2000cwb.googlegroups.com...> Yes the code you use to write equations is basically the same as TeX. > Thanks for going to it. Post some stuff! > > -Todd Smith > www.exampleproblems.com >Hi Todd, Surely I will frequent you forum... how did you put math into the PHPBB forum? I also want to luanch a forum that supports math... can I licence your invention? Thanks a lot!
Reply by ●July 30, 20052005-07-30
Yeah you're right. It's just a regular wiki linked to a regular phpBB. It's still the best place to go for graduate level math, though! www.exampleproblems.com - Graduate level math -Todd
Reply by ●September 25, 20052005-09-25
"kiki" <lunaliu3@yahoo.com> wrote> "quasi" <quasi@null.set> wrote > > On Sun, 24 Jul 2005 11:14:52 -0700, "kiki" <lunaliu3@yahoo.com> wrote: > > > >>... I am wondering if anybody has seen > >>a collection of mathematical tricks ranging from high school math up to > >>graduate school math? Any website, Internet resources, books that have > >>these > >>kind bags of tricks? If not, I may want to start collecting and compile > >>one > >>such resources.For HS math: The Art of Problem Solving by Sandor Lehoczky and Richard Rusczyk. Best, Abe
