Re: Replacement of Cardinality (ubiquitous ordinals)

On 08/01/2024 05:36 PM, Jim Burns wrote:

On 8/1/2024 3:28 PM, Ross Finlayson wrote:

On 08/01/2024 04:23 AM, Jim Burns wrote:

On 7/31/2024 8:30 PM, Ross Finlayson wrote:

On 07/31/2024 01:21 PM, Jim Burns wrote:

>

If I remember correctly,  your (RF's) name for
not.talking about
what's outside the domain of discussion
is hypocrisyᴿꟳ.
>
That sounds like you're delivering a value.judgment:
that we _should not_ not.talk about
what's outside the domain of discussion,
that we _should not_ for example, not.talk about
_all_ triangles when we discuss whether
the square of its longest side equals
the sum of the squares of the two remaining sides.

>

Yeah, my mathematical conscience demands that
hypocrisy is bad.

>
Bad why?

>
"Wrong", ....

>
It is wrong to treat claims about right triangles
as though they are claims about more than right triangles.
>

Definition usually expands,

>
The hypocrisyᴿꟳ of NOT expanding
  the definition of right triangle ABC
  to encompass triangles without right angles
leaves it NOT wrong that
a segment CH from right angle C
  perpendicular to and meeting side AB at H
makes two more triangles ACH BCH,
  which are both similar to ABC
  which, as similar triangles,
  have corresponding sides in the same ratio
so that
A͞H/A͞C = A͞C/A͞B
H͞B/B͞C = B͞C/A͞B
(A͞H+H͞B)⋅A͞B = A͞C² +B͞C²
and
  A͞B² = A͞C² + B͞C²  is NOT wrong.
>

hypocrisy is bad.

>
If it is, then it isn't for making things wrong,
  which is something hypocrisyᴿꟳ
  (not.talking about outside the domain)
doesn't do.
>
>

>
There is no "outside" the universe.