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.
RE[2]: quantum
by roblearns on Fri 22nd Mar 2013 20:05 UTC in reply to "RE: quantum"

Member since:
2010-09-13

Well, Infinity + 1 is larger.
Infinity isn't "The largest number" because there is no "largest." (That implies that it stops and there is nothing larger).

Infinity + 1 is larger than Infinity in the same sense as "The set of real numbers" is larger than "the set of whole numbers." Both are infinite in size, but Set of Real Numbers contains elements that aren't in the Set of Whole Numbers.

===>I can't help myself, while you are correct in that my statement was wrong - I admit defeat on that.

If I were to say to you, that in that I had this infinite set of whole numbers, plus I had the number 1.

I would still only have the infinite set of whole numbers, the number 1 is already included. I still fail to understand, how in the context of a child's game where you are attempting to say the highest number possibile and someone says infinity, how the number infinity plus 1 is larger.

Probably the correct answer is infinity is not a number, but a set of numbers. Therefore infinity plus 1 - if taken as infinity plus the number 1 - is just wrong, because infinity already included the number 1.

But if it means infinity but some number outside this set, then that is a larger set. A larger set - but not a larger number.

In reality, I'm going back and stating that in this game the word 'infinity' really did represent the largest number possible. It's a misuse of the word infinity - I get that now.

However it is absolutely unreasonable to me, to suggest the number 1 in the context of stating the largest number, is outside the set of numbers.

Edited 2013-03-22 20:13 UTC

RE[3]: quantum
by BeamishBoy on Sat 23rd Mar 2013 05:56 in reply to "RE[2]: quantum"
Member since:
2010-10-27

If I were to say to you, that in that I had this infinite set of whole numbers, plus I had the number 1.

I would still only have the infinite set of whole numbers, the number 1 is already included. I still fail to understand, how in the context of a child's game where you are attempting to say the highest number possibile and someone says infinity, how the number infinity plus 1 is larger.

Well, if you find it difficult to understand how this could be so in the context of the natural numbers, try thinking about it using a different set.

Think of the largest possible set you can (the number of elements in your set is something that a mathematician would call the cardinality of that set).

Each time you come up with a set containing a huge number of elements, I can counter you by constructing a set containing all of your elements, plus any other element that isn't already in your set. Thus I can construct a set containing an arbitrarily large number of elements; this is, in essence, one type of infinity.

Probably the correct answer is infinity is not a number, but a set of numbers.

No. Infinity is not a number; it's a concept.

RE[4]: quantum
by roblearns on Sat 23rd Mar 2013 09:49 in reply to "RE[3]: quantum"
Member since:
2010-09-13

"If I were to say to you, that in that I had this infinite set of whole numbers, plus I had the number 1.

I would still only have the infinite set of whole numbers, the number 1 is already included. I still fail to understand, how in the context of a child's game where you are attempting to say the highest number possibile and someone says infinity, how the number infinity plus 1 is larger.

Well, if you find it difficult to understand how this could be so in the context of the natural numbers, try thinking about it using a different set.

Think of the largest possible set you can (the number of elements in your set is something that a mathematician would call the cardinality of that set).

Each time you come up with a set containing a huge number of elements, I can counter you by constructing a set containing all of your elements, plus any other element that isn't already in your set. Thus I can construct a set containing an arbitrarily large number of elements; this is, in essence, one type of infinity.

Probably the correct answer is infinity is not a number, but a set of numbers.

No. Infinity is not a number; it's a concept.
"

I actually think you suffer from an understanding of language.

I can define a set as all possible numbers.

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

And infinity is a concept - I said that. You said that. You can pretend we are in disagreement, but we are not.