🚀 go-pugleaf

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