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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.

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*

Oh please do explain what those risks are - or would that be risky?

Seriously dude I was not representing myself as an expert - my words stating the opposite of that - did in fact represent what I mean, and weren't some clever ploy.

My explanatory style is meant to lay bare to the world what I might or may not understand on the subject, both to clarify my own thoughts and to invite commentary, and my experience has been that talking advances the subject more than being silent.

I appreciate the advice both the counterpoints on what quantum mechanics is about, and the little banter on the child's game of stating the largest number.

Peace, friend!

*Edited 2013-03-22 20:56 UTC*

Let me try to help you a bit understand what QM is and how it works.

One of the core tasks of physics is to describe what makes things move and how, whether the things in questions are tiny electrons or huge nebulas. Newton's laws of motion are a simple description of this which works pretty well at our scale, whereas Einstein's special and general theories of relativity are more accurate at high speed and large scales, and quantum mechanics (or QM) is the best at small scales.

QM and relativity can both be seen as extensions of Newton's laws to extreme scales, since if we try to apply them to "regular" objects, we'll get similar results as with Newton's laws. However, merging them into one single unified theory has proved to be extremely difficult for theoretical physicists. At this point, finding a satisfactory quantum description of gravitation, as described by the theory of general relativity, remains an open problem.

Now, how does the quantum description of the world differs from the one offered by classical mechanics? In a nutshell, it allows for some physical situations which are perfectly impossible in a Newtonian world, and simultaneously forbids some things which Newton's laws are perfectly fine with. Here are a few examples:

-Quantum objects' properties are not assumed to be perfectly known. What QM describes instead is the probabilities of finding something in a given state: at a given position, with a given speed...

-All these possible states of a system are not just statistical odds. Unless a measurement procedure leads the system to collapse in a single state, multiple "possible" states of a system exist simultaneously, and may thus interact with each other.

-QM's laws of motion are based on this latter effect, describing the probabilities of finding a system in a given state as changing in space and time in a manner similar to that a sound or like wave.

-All properties of a system are not independent, and it's impossible to simultaneously know all of them at once. This stem from the mathematics used to describe quantum states, which happen to be matching some real-world behaviors.

The reason why we're dealing with a theory that violates common sense in such a brutal way is that we have failed to find a saner description of the world which matches experiment so far. As an example, if the microscopic world followed Newton's laws of motion or their relativistic equivalents, electrons would crash into atom nuclei, many magnetic materials would have totally different properties, and we would still have to argue upon whether light is a wave or a stream of particles instead of having a maths that unify both descriptions.

*Edited 2013-03-22 21:07 UTC*

@Neolander, thanks for the explanation, although if I could request of you a more specific explanation of quantum computing, that would be great.

From my understanding regular computing would have to be based on the same laws of mechanics and properties of our world as everything else, its not as if we can step outside of it, simply because we are ignorant of it.

So, there must be something special about quantum computing that separates it from merely a theoretical description of how things work - to a practical engineering difference.

I'm not going to pretend that I didn't already go to wikipedia and try to make some sense of entanglement and superposition. The problem is - as much as they might try to be simple and easy to understand, they aren't quite using the right words for me.

Regular computers use transistors and attempt to represent information in binary, 1' and 0's. My understand is quantum computers attempt to use quantum properties to represent and manipulate data.

Ok, but then that's not enough to get it for me, and frankly I was joking earlier, but since you all are trying to help - what's the missing piece here?

It's not enough to just state the states can be 1, 0, or inbetween, what are the states, how do you manipulate them?

I can program in assembler just a little bit - so at least in my head, I get how regular computers work - shouldn't I be able to understand quantum computers. Lets say I want to program a quantum computer - what are my steps to do so?

Member since:

2010-09-13

My understanding was that quantum is just an adjective - allowing us to refer to the smallest possible discrete unit of something.

So the smallest possible unit of weight isn't 1 kilogram, because you can divide that into grams. Any number you define can be subdivided so you have to just bail on that scene, and just refer to quanta instead.

It's like the old child's game where you state the largest number, and finally someone says infinity, and then someone says infinity+1 - no dude, infinity is defined as the largest number, and quanta as the smallest discrete unit - as the infinitesimally small.

After this things get a bit murky, but apparently Einsteins theory of relativity and Quantum theory when taken together, can describe everything we know about matter and energy.

And you have other oddities like, Einsteins theory of relativity, Quantum Theory, and Selena Gomez, taken together somehow predicts the popularity of the 1990's hit Melrose place. A seemingly unrelated event.

Look, I don't want to be 'that guy' that guy that poo poo's everything he doesn't understand, and predicts everything to fail. because he doesn't get it. But I don't get it, and when I read all the people saying this is hocus pocus - what can I say, it seems like 'it kinda is' - they really need to make a bit more progress, then I'll take another looksy.