XPost: sci.logic, sci.math   
   From: janburse@fastmail.fm   
      
   Hi,   
      
   My attention mechanism is better than any AI.   
   Took me 2 seconds to spot the nonsense.   
      
   Because I know the internet cranks struggle   
   with the continuum only too good.   
      
   Among the classic internet cranks are:   
   - Archimedes Plutonium   
   - Ross Finlayson   
   - Who else?   
      
   Bye   
      
   Mild Shock schrieb:   
   > Hi,   
   >   
   > What you wrongly called Intermedite Value,   
   > where Value refers to the Value of a function,   
   >   
   > is only "dense order". Nobody calls it "gapless".   
   > Because in the case of Q it has still gaps.   
   >   
   > for x < y, there is z with x < z < y   
   > https://en.wikipedia.org/wiki/Dense_order   
   >   
   > For example Q has the irrational numbers as gaps.   
   >   
   > Bye   
   >   
   > Mild Shock schrieb:   
   >> 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)   
   >>>>   
   >   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)