Re: Incompleteness of Cantor's enumeration of the rational numbers

On 11/4/2024 4:07 PM, Moebius wrote:

Am 05.11.2024 um 00:08 schrieb Chris M. Thomasson:

On 11/4/2024 2:02 PM, Jim Burns wrote:

On 11/4/2024 3:54 PM, Chris M. Thomasson wrote:

On 11/4/2024 6:37 AM, Jim Burns wrote:

>

Further there are never
two irrational numbers
without an interval between them.

>
Unless they equal each other? ;^)

>
And thus are one, not two, points?
>
>

Well, yeah in a sense.
>
A = (-1, .5, 3, 7)
B = (-1, .5, 3, 7)
>
A = B = true

>
Well, rather:
>
    "A = B" is true.
>
After all, (-1, .5, 3, 7) =/= true (I'd say). :-P
>
__________________________________________________
>
Actually, some authors would prefer to write:
>
"there are never two different irrational numbers without an [nonempty] interval between them".
>
It's a matter of "style" or "precision", if you like.
>
If we talk about "two" real numbers x, y [in math], usually x = y is NOT excluded.
>
For example,
>
        for any two real numbers x, y ... bla bla
>
USUALLY does not exclude x = y. [Might look strange, but is just the usual math lingo.]

 If A = B then they are equal? For instance 5=5, the self relation equality? lol.