# [r-t] Re: Proofs

R.P.I. Lewis mapc01 at bangor.ac.uk
Tue Sep 28 11:12:32 UTC 2004

```> I'm beginning to wish I hadn't got along with Philip's suggestion.

Sorry, I was just making a suggestion (I would not have mentioned it but I
did not understand the last part of what you wrote, and I thought while i
was asking what it meant I'd add it in, in case someone was interested..)
I did not realise it would upset you!

> X(AC) here means just the falseness between A & C - no 'direction' is
> intended but having decided on the rule 'inverse of second of the pair
> operating on the first of the pair', we're stuck with it.

if there was really no direction then why do we not get X(AC)=X(CA)? Seems
to me that the fact that X is not symmetric tells us something

>
> My wife, who, to save her from ennui, is currently doing
> an M.Math course at the Open U (M336) confirms my recollection from 30 years
> ago that the convention (then and now) is that 'ab' is 'a operating on b'
> or, if you like as I say sotto voce when I write it down, 'a of b'.

It rerally depends on what "operating on" means.  there are left
operations and right operations, and a group operates on itself by both
left multiplication and right multiplication.  Actually left and right
actions are a separate issue to the convention for how you write group
multiplication,

>
> In fact, the whole analysis is just as valid the other way round, C.inv(A),
> except that it might be less natural when starting from first principles.
>
> The definition of J in words is the permutation  for a seconds place lead

as in "J=12"? Is this a standard notation, and if so where should I have
looked to find this out for myself?

> end so:
>
> > e = rpJ => rp = J
> >
> >Here you meant to type "e = rpJ => pr = J" I suppose
>
> No! - since J is self-inverse, it makes no difference: J = pr = rp.
>

Oh OK, I did not realise that J was a place notation.

> Anyway, I said in the pre-amble:
>
> "An asymmetric section may also have just one falseness group."
>
> Inspection of the appropriate collection will show that it is usual for any
> asymmetric section to lead to  two distinct falseness groups.

ah... when you say "falseness groups" you don't mean a group in the
mathematical sense, you just meant letters? sorry, this confused me... I
*thought* that what you were doing was to take the values of X and
generate a subgroup, (which would hopefully tell us something about the
method)

Just goes to show that people who talk maths don't have the monopoly on
confusing people with undefined terms...

```