Re: There is a first/smallest integer (in Mückenland)

On 7/20/24 8:47 AM, WM wrote:

Le 19/07/2024 à 20:52, Jim Burns a écrit :

On 7/19/2024 9:53 AM, WM wrote:

 

Then we can abbreviate each and every x > 0 by (0, oo).

>
Your "abbreviating" is a quantifier shift.
Making it less visible doesn't make it prove anything.

 My theorem: X is left-hand side of every x > 0 <==> X is left-hand side of (0, oo).
Find a counter example or accept it.
If you believe it can be interpreted as a quantifier shift, then note that not every quantifier shift produces a wrong result. Example: see above.

>
"Abbreviate" rock.paper.scissors and
you get wrong answers.
That method is unreliable.

 Don't waffle, do what is usual in mathematics: Show a counter example for my theorem.
 Regards, WM

But no value of x can BE that left hand side of (0, oo) because if such an x did exist then x/2 would be outside the interval, but also positive.
The fact being that these systems are UNBOUNDED, and thus there does not exist a number "next to" another number, but we just have an infinite density of numbers.