XPost: sci.logic, sci.math   
   From: janburse@fastmail.fm   
      
   Hi,   
      
   John Gabriel always said there is something   
   bogus in mainstream calculus. Maybe he spotted   
   something here:   
      
   IVT + EVT + differentiability ⇒ Rolle's Theorem ⇒ MVT.   
      
   Is ZF really enough, don't we need ZFC_omega:   
      
   https://en.wikipedia.org/wiki/Axiom_of_countable_choice   
      
   Don't remember. This was "hot" during:   
      
   Hermann Weyl (“Das Kontinuum”, 1918)   
   Do as much of classical analysis as possible   
   predicatively. Weyl could do IVT + EVT,   
   but he didn't get MVT, right?   
      
   Early Saul Kripke (1950s/1960s manuscripts   
   In the 1960s–70s, Kripke (and also Feferman) studied   
   systems for analysis based on ramified analysis   
   or predicative provability.   
      
   Weyls workaround:   
   Lipschitz (or uniform modulus) conditions.   
      
   Bye   
      
   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   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)