Linked by Thom Holwerda on Fri 22nd Mar 2013 10:02 UTC

"But a powerful new type of computer that is about to be commercially deployed by a major American military contractor is taking computing into the strange, subatomic realm of quantum mechanics. In that infinitesimal neighborhood, common sense logic no longer seems to apply. A one can be a one, or it can be a one and a zero and everything in between - all at the same time. [...] Now, Lockheed Martin - which bought an early version of such a computer from the Canadian company D-Wave Systems two years ago - is confident enough in the technology to upgrade it to commercial scale, becoming the first company to use quantum computing as part of its business." I always get a bit skeptical whenever I hear the words 'quantum computing', but according to NewScientist, this is pretty legit.

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Member since:

2008-10-26

BeamishBoy is arguing from the standard construction of numbers and set in modern mathematics which, for somewhat subtle reasons, disallows defining the set of all possible numbers. Due to the simplifying assumption that everything is a set (otherwise you could run out of numbers for talking about the size of sets which is similar to the argument BeamishBoy makes in his sibling post), numbers are defined in such a way that the set of all possible numbers must contain itself and sets containing themselves is disallowed due to https://en.wikipedia.org/wiki/Russell%27s_paradox .

This means that there is obvious way to define the largest infinity and leads to two separate kinds of numbers which act rather differently for infinities:

https://en.wikipedia.org/wiki/Ordinal_numbers for counting things where n != n+1 even n is infinite and https://en.wikipedia.org/wiki/Cardinal_numbers for measuring the size of sets where n == n+1 if n is infinite.