08/17/2012, 03:18 PM
the problems with § are in general not having desired properties and incomplete definitions.
to list the most important
1) define §-x
2) -a§b =?= b§-a ? see 1)
-a§b = -1 * a§b for a > b > 0 but otherwise ?
hence commutativity might not hold. and even anticommutativity might not hold.
3) associativity does not hold and is not defined
(1§1)§2 = 0§2 = §2
1§(1§2) = 1§§1 ??? what ?? = 0 ,? 0=/= §2 either
(3§3)§2 = §2
3§(3§2) = 3§1 = 2 =/= §2
inconsistancy^2 !
4) we lost linearity because -1§1 = 1§1
5) the § does not have a unique defined inverse operator see 4)
6) distributivity does not hold
§1*(-1+1) = §1*0 = 0
but §1*-1 = 0 and thus §1*-1 + §1*1 = §1 =/= 0 !!
7) you use § both as an operator and a sign.
that is valid for - but seems troublesome here.
a§§b = ?? a§§§c = ?? ( see also above )
what is §1^2 ?
9) what is 1/§x ??
10) what is log(§2) ??
11) it is clear from the above that we cannot use taylor series and calculus without worries on these objects ... if they even exist.
since we do not have much properties to work with , the general objection is it is random without structure and thus might never solve anything WITH STRUCTURE because it doesnt have it itself.
using special cases just seems to reduce to the reals and then we have jmsnx operator mentioned earlier which is as classic as can be.
regards
tommy1729
to list the most important
1) define §-x
2) -a§b =?= b§-a ? see 1)
-a§b = -1 * a§b for a > b > 0 but otherwise ?
hence commutativity might not hold. and even anticommutativity might not hold.
3) associativity does not hold and is not defined
(1§1)§2 = 0§2 = §2
1§(1§2) = 1§§1 ??? what ?? = 0 ,? 0=/= §2 either
(3§3)§2 = §2
3§(3§2) = 3§1 = 2 =/= §2
inconsistancy^2 !
4) we lost linearity because -1§1 = 1§1
5) the § does not have a unique defined inverse operator see 4)
6) distributivity does not hold
§1*(-1+1) = §1*0 = 0
but §1*-1 = 0 and thus §1*-1 + §1*1 = §1 =/= 0 !!
7) you use § both as an operator and a sign.
that is valid for - but seems troublesome here.
a§§b = ?? a§§§c = ?? ( see also above )
what is §1^2 ?9) what is 1/§x ??
10) what is log(§2) ??
11) it is clear from the above that we cannot use taylor series and calculus without worries on these objects ... if they even exist.
since we do not have much properties to work with , the general objection is it is random without structure and thus might never solve anything WITH STRUCTURE because it doesnt have it itself.
using special cases just seems to reduce to the reals and then we have jmsnx operator mentioned earlier which is as classic as can be.
regards
tommy1729