• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 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, 07:14 AM (This post was last modified: 06/03/2008, 07:18 AM by Ivars.) To put it shorter: Can we construct a function defined on all set of hyperreals or subset of them ( or superreals )which would preserve the property: REAL f( subset of hyperreals) = such that f(h(x)^h(y)) = f( h(x)) * f(h(y)) for all x, y>=0 Where h(x), h(y) is the subset of hyperreals relevant to the problem and the same for all x, y- what ever x, y, the subset of hyperreals we can use to construct such function does not change. This requires that it is possible to establich one to one correspondence between subset of hyperreals and real numbers, or, at least, 2 real numbers 1 and 0. In my simple thinking, it requires only 2 hyperreals besides each real to do that- as indicated in previous post. I wonder also how to extend this to hyper imaginaries as there is not reason they can not exist, so they must exist. If true, such function would perform the necessary transformation required from 3_log. If so , that would allow simple generalization to n_log, (n,m)_log by just adding more scales of numbers , like 2_hyperreals which are formed by 2 neighbouring hyperreals , between them, 3_hyperreals formed from 2 neighbouring 2_hyperreals etc. The nice thing is, surreal numbers of Conway are constructed exactly in such way, so that field has been already covered very deeply, with all ordinalities , cardinalities calculated and proved. 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

 Possibly Related Threads... Thread Author Replies Views Last Post The AB functions ! tommy1729 0 1,604 04/04/2017, 11:00 PM Last Post: tommy1729 the inverse ackerman functions JmsNxn 3 5,999 09/18/2016, 11:02 AM Last Post: Xorter Look-alike functions. tommy1729 1 2,078 03/08/2016, 07:10 PM Last Post: hixidom Inverse power tower functions tommy1729 0 1,920 01/04/2016, 12:03 PM Last Post: tommy1729 [2014] composition of 3 functions. tommy1729 0 1,813 08/25/2014, 12:08 AM Last Post: tommy1729 Intresting functions not ? tommy1729 4 5,184 03/05/2014, 06:49 PM Last Post: razrushil generalizing the problem of fractional analytic Ackermann functions JmsNxn 17 22,354 11/24/2011, 01:18 AM Last Post: JmsNxn Discrete-analytic functions Ansus 4 5,752 07/30/2011, 04:46 PM Last Post: tommy1729 product functions tommy1729 5 6,512 06/01/2011, 05:38 PM Last Post: tommy1729 Periodic functions that are periodic not by addition JmsNxn 0 2,791 04/17/2011, 09:54 PM Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)