Linked by Thom Holwerda on Fri 22nd Mar 2013 10:02 UTC
Hardware, Embedded Systems "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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RE: later
by Chris_G on Sun 24th Mar 2013 12:03 UTC in reply to "later"
Chris_G
Member since:
2012-10-25

“So infinity +1 has no additional meaning.”

If the infinities in both cases are equal, then yes it does. Different size infinites are one of the fundamental principals of calculus. It's also one of the most difficult to understand.

Don't think in terms of sets where each number can only be used once. That's a purely artificial restriction that has absolutely no meaning whatsoever in this context. If you have a set of all reals, for example, you have a set with infinite members, none of which has a value of infinity. We are actually talking about infinite series. Not sets.

Lets say we have the following summation,

S1 = 1+2+3+4 + · · ·

We can all agree that the above goes to infinity. Now lets compare it with the following series,

S2 = 2+4+6+8 + · · ·

so that each number in the series is 2*n. Both are infinite. However, S2/S1 is exactly 2.

Because each term in S2 is divisible by 2, it is absolutely correct to write,

S2 = 2*(1+2+3+4 + · · ·)

In S2/S1 the series cancel out, their value (infinite or otherwise) is completely irrelevant.

S2, despite being infinite, is *exactly* twice S1, which is also infinite.

Whether a number has already been used is irrelevant. It's a sum. I can add the same value any number of times.

1+1+2+3+4 + · · · > 1+2+3+4 + · · ·

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