🚀 go-pugleaf

On Nov 22, 9:53 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Nov 22, 3:58 pm, Zuhair <zaljo...@gmail.com> wrote:
>
>
>
> > On Nov 22, 5:45 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > On Nov 22, 11:48 am, Zuhair <zaljo...@gmail.com> wrote:
>
> > > > On Nov 21, 11:41 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > > > On Nov 21, 8:34 pm, Zuhair <zaljo...@gmail.com> wrote:
>
> > > > > > > > For all x : (x)
>
> > > > > > > then (name) =/= name
>
> > > > > > where is the objection? I don't see it
>
> > > > > (a U a) =/= (a)
>
> > > > > in your system
>
> > > > It is the same in ordinary way of writing logic. (a U a) = a
> > > > (a U a) doesn't equal (a), similarly U(a,a) = a and it is
> > > > not the case that U(a,a) = (a). All of this is present
> > > > in ordinary logic.
>
> > > congratulations on joining the OUTRIGHT LIAR CLUB SCI.MATH
>
> > > > > Your system is more complicated to parse into a formal syntax because
> > > > > "(" has multiple meanings.
>
> > > > > You could possibly use {x}{y}[z] z>(x+y)
>
> > > > > then there is no confusion as the parenthesis "("
> > > > > retains it's single purpose of prioritising reduction.
>
> > > > > but the set { a | f(a) } the curly braces now have a double meaning
>
> > > > > although FORALL(x) = {x} is a better match.
>
> > > > > {x} = ALL x  (set of all x)
> > > > > [x] = EXIST x  (instance of x)
>
> > > > > (y) = y  (standard parenthesis)
>
> > > > > I think curly braces is better for forALL!
>
> > > > NO curly braces have their own usage, {x} denotes the singleton set
> > > > of x, so it is not appropriate here.
>
> > > if none of you are capable of listening then none of you will be
> > > spoken to.
>
> > > what rot!
>
> > > Herc
>
> > Possibly I was a little bit dense about that,
> > I think what you meant to say is
>
> > we have:  a U a = a
>
> > if we put each side in brackets then we will get
>
> > (a U a) = (a)
>
> > but with my notation this cannot be done liberally
> > since this would mean (a U a) = for all a. Ok, that's
> > a fine argument. But the context of matters will
> > serve to differentiate this situation from a quantifier.
> > From the human side it is easy to differentiate matter
> > however possibly for a computer program this would
> > cause some confusion.
>
> > That's a good argument though. However there *is*
> > a difference, when (a) represents a quantifier
> > it must be followed by a bracket that is the opening
> > bracket of the scope of quantification so it is in reality
> > (a) (...), , however as an abbreviation we may
> > drop the following opening bracket in some situations
> > like when it is followed by a quantifier also like: (a) (b) (...)
> >  On the other hand, the case of (a) representing just
> > a bracketed single variable a (that may result from
> > bracketing a function) then there is no brackets
> > of quantification following it. If you use the dot notation
> > you can also differentiate them. Sorry for not paying
> > attention to this argument.
>
> > Thanks for this observation
>
> > Zuhair
>
> Ah right!
>
> Well there's nothing wrong with (a)[b] b>a
>
> and if it's adopted then I'd have no problem using it.
>
> But as far as a concise formal notation it's still problematic
> and only reduces the character count slightly from
>
> A(a) E(b) b>a
>
> which is distinguishable from matrix, calculus and other branches
> where (a) [b] have their standard meanings.
>
> So it might not be good enough to be logically concise, it should be
> mathematically concise.
>
> If you use A(x) E(x) then you are not introducing any special system
> at all!
>
> A(Variable, Predicate) is just a 2 place FUNCTION where
> Predicate holds true for all values of Variable.
>
> A(x, x=x+1-1)
> A(x)(x=x+1-1)  CURRIED FUNCTION A
> A(x) x=x+1-1   SHORTHAND CURRIED FUNCTION A
>
> so A(x) is not any Standard, it's just a reserved_function_name for
> the forALL function A().
>
> I agree AxEy is too informal, but A(x) works well (as a reserved
> function)
>
> eg.
>
> If Ln is a List with oo-many of all digits in every digit position
> and Ln' is a different ordered List of the same set of reals in Ln
>
> A(L1) A(L2) E(L1') E(L2')
> DIAGONAL(L1') = DIAGONAL(L2')
>
> Uncountability Vanquished!
>
> Herc

Ok, i think I reached to a beautiful way of treating brackets using
what is
available at the ordinary keyboard sets.

for universal quantification I shall use the curved brackets ( )

so for all x. phi will be written as (x) (phi)

while for Existential quantification I shall use the straight brackets
[]

so Exist x. phi will be written as [x] [phi]

This cuts a lot of confusion and it visually helps to see how the flow
of matters is going in complex formulas.

However precedence brackets shall be reserved to ( ).

So back to your notation

A (x , x=x)

which is written as A(x) (x=x)

Here with my notation this would be written as

(x) (x=x)

while

E (x, x=x)

which is written as  E(x) (x=x)

would here be written as

[x] [x=x]

Anyhow I see my notation a little bit more elegant.

Zuhair