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:

2010-10-27

I can define a set as all possible numbers.

And then you cannot tell me there is an additional number outside the set.

Perhaps (I'd actually dispute that by asking you precisely what type of numbers are in your set, but I digress).

Regardless, let me be kind and assume that you've got a set of numbers that is uncountable; perhaps you're thinking of, say, the set of all real numbers. You're now quite pleased with yourself because you've got a set with an infinite number of elements.

However, I come along and claim that I can define a set with even more elements in it than yours. I can even be kind to you and say that I'll restrict myself to working with a set containing real numbers. The question therefore is: do you believe that I can construct a set of real numbers that contains more elements than your - already infinitely large - set of real numbers?

Because I can do so quite simply by taking my set to consist of all possible subsets of the real numbers. Both of our sets have infinitely many elements, but mine has more than yours.