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 Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 06/03/2008, 08:49 AM (This post was last modified: 06/03/2008, 08:51 AM by Ivars.) bo198214 Wrote:@Ivars: this proof also works for hyperreals. Based on "language analogy" between real and hyperreal sets? I will look into this deeper before making any new statements. At least, as a first step, is it possible to construct such discontinuos function f(x) on real numbers which in each point $x_o$ is 0 if the point is approached from left, and 1 if approached from right( or vice versa)? So: $\lim_{x\to\\{-x_o}} f(x_o)= 1,$ $\lim_{x\to\\{+x_o}} f(x_o)= 0,$ Alternatively : $\lim_{x\to\\{-x_o}} f(x_o)= 0,$ $\lim_{x\to\\{+x_o}} f(x_o)= 1,$ Can we define a discontinuous function in such manner? The one use of such function as a function of $x_o$ would be for any $x_o$ to discern from which side we are approaching it. If we approach $x_o$ from left, this function $f(x_o)$ has value e.g. 0 (alternatively 1) if we approach $x_o$ from right ,this function $f(x_o)$ has value e.g. 1 (alternatively 0) Ivars « Next Oldest | Next Newest »

 Messages In This Thread Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 06/01/2008, 01:54 PM only identity maps powers to products - by bo198214 - 06/01/2008, 03:01 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 06/01/2008, 05:02 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by andydude - 06/02/2008, 04:46 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by bo198214 - 06/03/2008, 08:09 AM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 06/03/2008, 08:49 AM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by bo198214 - 06/03/2008, 01:13 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 06/03/2008, 01:22 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by bo198214 - 06/03/2008, 03:21 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 06/02/2008, 07:15 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 06/03/2008, 07:14 AM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 06/03/2008, 03:34 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by bo198214 - 06/03/2008, 05:14 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 06/03/2008, 09:45 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by andydude - 06/04/2008, 01:51 AM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 06/04/2008, 07:20 AM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by bo198214 - 06/04/2008, 02:14 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 06/04/2008, 02:33 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by BenStandeven - 05/12/2009, 01:00 AM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by Ivars - 12/04/2008, 01:15 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by JmsNxn - 04/14/2011, 11:16 PM RE: Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp - by bo198214 - 04/15/2011, 07:29 AM

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