Re: Replacement of Cardinality (ubiquitous ordinals)

On 8/1/2024 8:52 PM, Ross Finlayson wrote:

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.

Yeah, my mathematical conscience demands that
hypocrisy is bad.

>
Bad why?

>
"Wrong", ....
Definition usually expands,

It sort of seems the straw-man of you
to say I'm disputing Pythagoras
when all I did was point out that
Russell was more-or-less lying to you.

This is the heart of the matter:
Expanding the definition of right triangle
does not dispute Pythagoras.
Expanding the definition of right triangle
moves us to a second conversation.
Pythagoras is in the first conversation.
The second has no effect there.
First conversation.
⎛ Consider △ABC and AC⟂BC
⎜
⎜ H in AB:  CH⟂AH and CH⟂BH
⎜
⎜ △ACH ∝ △ABC
⎜ A͞H/A͞C = A͞C/A͞B
⎜
⎜ △CBH ∝ △ABC
⎜ H͞B/B͞C = B͞C/A͞B
⎜
⎜ (A͞H+H͞B)⋅A͞B = A͞C² + B͞C²
⎝ A͞B² = A͞C² + B͞C²
Second conversation.
⎛ Consider △ABC ...
⎜ Comrades!
⎜ Throw off the shackles of the past!
⎜ AC⟂BC  or  AC̸⟂BC
⎜ You have been lied to.
⎜ For A͞B = A͞C = B͞C
⎜ A͞B² ≠ A͞C² + B͞C²
⎝ Freedom!
I am exaggerating for effect.
If you have called the rest of us comrades, etc,
I have missed it.
Nor do I think that you dispute Pythagoras.
I hope that you do not.
I want you to come over to our side and
look at the shape of your argument once more.
Are non.standard right triangles
an objection or a change of topic?
Is non.standard analysis
an objection or a change of topic?
Would you like to know why
your objections to a vast swath of of mathematics
attract such a tiny bit of attention?
No one else perceives what you're doing
to be raising an objection.
In my own case, it took me years
to guess that's what you intend.