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lemmington_steele @lemmy.world
Posts 2
Comments 74
EDIT: I THINK I STAND CORRECTED
  • technically yes, but the proof would usually show that this works by constructing the bijection of [0,1] and (0,1) and then you'd say the cardinalities are the same by the Schröder-Berstein theorem, because the proof of the latter is likely not something you want to demonstrate every day

  • EDIT: I THINK I STAND CORRECTED
  • no, there aren't enough integers to map onto the interval (0,1).

    probably the most famous proof for this is Cantor's diagonalisation argument. though as it usually shows how the cardinality of the naturals is small than this interval, you'll also need to prove that the cardinality of the integers is the same as that of the naturals too (which is usually seen when you go about constructing the set of integers to begin with)

  • EDIT: I THINK I STAND CORRECTED
  • actually you can for each real number you can exhaustively map a uninque number from the interval (0,1) onto it. (there are many such examples, you can find one way by playing around with the function tanx)

    this means these two sets are of the same size by the mathematical definition of cardinality :)

  • Why are CAs important if anyone can get their certificate signed for free?

    For example, anyone could use Let's Encrypt to get a trusted certificate, so what makes this trustworthy? Or why not trust everyone that signs their own certificates with a program like OpenSSL?

    10

    Why do SSDs have a more limited number of times data can be written to them, but RAM memory can handle loads of re-writes?

    In a similar vein, why can we not use the technology of RAM to prolong the life-cycle of an SSD?

    39