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   sci.physics      Physical laws, properties, etc.      178,769 messages   

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   Message 178,137 of 178,769   
   Stefan Ram to Stefan Ram   
   Re: continuity and topological spaces   
   26 Aug 25 14:53:35   
   
   From: ram@zedat.fu-berlin.de   
      
   ram@zedat.fu-berlin.de (Stefan Ram) wrote or quoted:   
   >  . The inverse "r" has the value columns swapped:   
   >   
   >r   
   >x y   
   >3 1   
   >3 2   
   >   
   >  This "r" is a relation, but not a function.   
   >   
   >  Wikipedia: "The inverse of 'f' exists if and only if 'f'   
   >  is bijective". The "f" from above is not bijective (because   
   >  it's not injective), so the inverse of "f" does not exist.   
      
     Above, I'm using "the inverse" and then later write,   
     "the inverse of 'f' does not exist.", which is a bit   
     inconsistent. So, it should be:   
      
   |  . The inversion "r" has the value columns swapped:   
   |   
   |r   
   |x y   
   |3 1   
   |3 2   
   |   
   |  This "r" is a relation, but not a function.   
   |   
   |  Wikipedia: "The inverse of 'f' exists if and only if 'f'   
   |  is bijective". The "f" from above is not bijective (because   
   |  it's not injective), so the inverse of "f" does not exist.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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