Example of IVT leading to Irrational Numbers (Was: Rossy Boy roasted by Kimi [Intermediate Value Theorem Wrong])

From	Mild Shock <janburse@fastmail.fm>
Newsgroups	sci.logic, sci.math, sci.physics.relativity
Subject	Example of IVT leading to Irrational Numbers (Was: Rossy Boy roasted by Kimi [Intermediate Value Theorem Wrong])
Date	2025-11-14 00:39 +0100
Message-ID	<10f5q72$1g6t$1@solani.org> (permalink)
References	(5 earlier) <tQqdndRUx9FXEY70nZ2dnZfqn_di4p2d@giganews.com> <sJ6cnQlY6aHgNI70nZ2dnZfqnPGdnZ2d@giganews.com> <XXednaAyesFCNo70nZ2dnZfqn_di4p2d@giganews.com> <FPCcnYKDAtgSx4v0nZ2dnZfqn_Zi4p2d@giganews.com> <10f5pn8$1g2m$1@solani.org>

Cross-posted to 3 groups.

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Hi,

Take a = 1 and b = 2 with this function:

f(x) = x^2 - 2.

https://en.wikipedia.org/wiki/Intermediate_value_theorem

Now take s = 0, what is x ?

Mild Shock schrieb:
> Hi,
> 
> Looks like Kimi was grilling you with no
> mercy. I guess you got a complete roast.
> 
> BTW: You got Intermediate Value Theorem
> theorem wrong. Its not about a 'c' such
> that 'a < c' and 'c < b'.
> 
> The important thing is there is also
> a function f involved. In particular a
> continuous function.
> 
> Have Fun!
> 
> Bye
> 
> Ross Finlayson schrieb:
>> Gaplessness (intermediate-value) inside ZF
>>
>> “IVP_d” ≡ ∀a,b∈E_d ∀k∈d+1 (a ≺_d b → ∃c∈E_d (c=part_d(k) ∧ a ≼_d c ≼_d 
>> b))
>> ZF ⊢ ∀d≥1 IVP_d  (finite intermediate-value property)
>>

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Example of IVT leading to Irrational Numbers (Was: Rossy Boy roasted by Kimi [Intermediate Value Theorem Wrong]) Mild Shock <janburse@fastmail.fm> - 2025-11-14 00:39 +0100
  The technical term is only "dense order" (Was: Example of IVT leading to Irrational Numbers) Mild Shock <janburse@fastmail.fm> - 2025-11-14 00:41 +0100
    My attention mechanism is better than any AI [For Internet Cranks] (Was: The technical term is only "dense order") Mild Shock <janburse@fastmail.fm> - 2025-11-14 00:45 +0100
      Re: My attention mechanism is better than any AI [For Internet Cranks] (Was: The technical term is only "dense order") Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-11-14 05:58 -0800
        Who else , John Gabriel [MVT Locus caeruleus] (Was: My attention mechanism is better than any AI [For Internet Cranks]) Mild Shock <janburse@fastmail.fm> - 2025-11-14 17:55 +0100
          IVT + EVT gives MVT via Rolle [Using Superintelligence by the Speed of Light] (Was: Who else , John Gabriel [MVT Locus caeruleus]) Mild Shock <janburse@fastmail.fm> - 2025-11-14 18:05 +0100

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