XPost: sci.logic, sci.math   
   From: janburse@fastmail.fm   
      
   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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