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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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