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# How big an infinity?

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Tyockell said:

huh...scratches my head wtf is goin on??

Goddammit! You've got your dandruff all over me!

Almost totally unrelated, but certainly not worth a new thread

1/3 = 0.3333333....
2/3 = 0.6666666....

so 1/3+2/3 = 0.9999999....

so 1 = 0.9999999....

A better example:
There are an infinite number of decimal values between 0 and 0.1
Likewise, there are an infinite number of decimal values between 0 and 1.0

Both sets are infinite, but the set of x where 0 < x < 0.1 is a part of the set y where 0 < y < 1.0. The two sets are not completely identical, so the set x is by definition smaller than set y.

Huh, the new HTML option for admins & supermods mucks up those left-carats a bit.

What does infinity mean?

Infinity means, that if you were travelling, whether it's Concorde or sitting on a beam of light, you'd never come to the end.

Is it a number?

No.

Is it more or less than a million million million million million million million million million million?

More. Because you can always add 1 on to the end.

OK, I add a MILLION on the end.

Million million million million million million million million million million million million.
There is NO end, there is no end, by defenition..

Even if I carry on saying that all day?

What happens if I use "zillion"?

It'll have no effect..

Quillion?

No effect..

There ISN'T anything bigger than a quillion.

The principle is, that what ever number you try to think of, no matter how big it is, I could always come along and say "I've got a number which is 1 bigger".

And THAT number is.. infinity?

No.

IMJack said:

A better example:
There are an infinite number of decimal values between 0 and 0.1
Likewise, there are an infinite number of decimal values between 0 and 1.0

Both sets are infinite, but the set of x where 0 < x < 0.1 is a part of the set y where 0 < y < 1.0. The two sets are not completely identical, so the set x is by definition smaller than set y.

The sets x and y are equal in size (infinite) and also equal in cardinality (x[n] = y[n] / 10, y[n] = x[n] * 10). At least that's what I think, someone correct me if I'm wrong.

Ever noticed how maths teachers eventually trend towards wearing flood-victim clothes and smelling faintly of whiskey?

Explained, I think.

pritch said:

Wtf? Obviously they are both equally infinite. One is simply more occurant.

exactly. i don't know what this cardinality thing is about though heh.

Infinity is how many times an idiot turns over a keychain that says "How do yo keep an idiot busy all day? Flip Over."

Getting back to the original question, I would have to say that the amount of possible numbers will always be greater than the number of prime numbers, infinite or not. That's just how it is. Here's why: Let's say the numbers went up to 5. Of those five numbers, only four are prime, thus there are more prime numbers than there are normal numbers. It's as simple as that, and the amount of prime numbers only continues to fall behind after that. Now, the most important point is that with the infinite number of numbers and the infinite number of primes, no number on the list of primes can ever exceed the value of a number on the list of normal numbers. It's just not possible. For a number to be a prime, it must also be a number, thus it and every number preceeding it must be counted in the number of numbers.

Both lists may go on infinately, however, that merely means that the number of numbers is infinately more than the number of primes. They are both infinate, but one has more numbers than the other, and is thus larger.

EllipsusD: You're wrong, for the same reason almost everybody else is: you're making the assumption that infinity is (or behaves just like) a regular number and that two infinite numbers can be compared in size just like normal numbers. Specifically:

Now, the most important point is that with the infinite number of numbers and the infinite number of primes, no number on the list of primes can ever exceed the value of a number on the list of normal numbers.

"No number can exceed" is only true for finite numbers. When you've reached an infinite normal number, the prime number will also be infinite. And you can't do a regular > comparison of two infinite numbers.

Your example holds for every finite number, but it does not for infinite numbers.

Read what I wrote earlier in this thread: the only way two infinite sets can be of a different size (in any abstract sense of the word size) is by not being pairable.

fradrik is teh geniuz! heh, i think the main problem people are having here is that they don't understand infinity isn't just some really big number.

Fredrik said:
EllipsusD: You're wrong, for the same reason almost everybody else is: you're making the assumption that infinity is (or behaves just like) a regular number and that two infinite numbers can be compared in size just like normal numbers.

Perhaps, but I feel that you are wrong in assuming that infinite is a number at all. Rather, is it simply a way of saying that there is no end to the amount of numbers that can be.

Specifically:"No number can exceed" is only true for finite numbers. When you've reached an infinite normal number, the prime number will also be infinite. And you can't do a regular > comparison of two infinite numbers.

Your example holds for every finite number, but it does not for infinite numbers.

Infinite numbers, or rather infinity, is composed of finite numbers. Infinity is saying that there can always be more finite numbers, and there is no limit to how many finite numbers there can be. Thus inifinity is a never-ending collection of finite numbers and can just as easily be treated as such. What I meant by the statement that you quoted from me is that if there is a 151 as a prime number it, due to it's nature as a number must be a normal number as well. The next prime would be 153, right, but the list of normal numbers doesn't just stop at 151... due to the fact that 153 is recognized as a prime it must also be recognized as a number in general, and so the list of normal numbers must also go up to 153.

The only part about this that can be confusing is that the list of numbers can never end due to the definition of infinite, but let me bring up again the point I made: since infinity in the case has to do with numbers, and due to the definitional differences between normal and prime numbers, not only are the lists of numbers infinite, but the difference between the amount of normal numbers and the amount of prime numbers is also infinate. Thus, the amount of normal numbers is not only bigger than the amount of infinite numbers, but it is infinatly bigger.

EllipsusD said:

Infinite numbers, or rather infinity, is composed of finite numbers. Infinity is saying that there can always be more finite numbers, and there is no limit to how many finite numbers there can be.

Wrong, not infinity at all. Like saying there's no limit to how many runs can be scored in a baseball game. To say "You can score an infinite number of runs" is incorrect. You're confusing infinite with indefinite.

Infinity = number with no end. Endless number. Nothing less than an endless number.
Indefinity = Limitless. No maximum. Cannot be limited.

What you were referring to was indefinity, not infinity.

AndrewB said:
Wrong, not infinity at all. Like saying there's no limit to how many runs can be scored in a baseball game. To say "You can score an infinite number of runs" is incorrect. You're confusing infinite with indefinite.

Infinity = number with no end. Endless number. Nothing less than an endless number.
Indefinity = Limitless. No maximum. Cannot be limited.

What you were referring to was indefinity, not infinity.

If I may, the Merriam-Webster dictionary defines infinity as being an indefinately great number or amount. In that sense infinity is comprised of indefinity. I assume that for an arguement you could define infinity as being a number (though I can find no definition to support that), but I am, for my arguements, using it as an amount of numbers. A quantifier so to speak.

Oh, and by the way, the statement "You can score an infinite number of runs" is definitionally correct. Look it up for yourself if you don't believe me.

Standard dictionaries aren't generally very reliable when it comes to precise definitions of mathematical terms. If you're really interested, I can personally recommend A handbook of terms used in algebra and analysis (Howson) - no BS and straight to the point (it saved my ass countless times at university). But that site we've been linking to is pretty good too.

Anyway, no one should be embarrassed about finding infinity a difficult concept - it's one of those things that seems to become more confusing the more you learn about it.

A set is said to be finite if the only subset of X which is equipotent to X is X itself. A set which is not finite is said to be infinite.

So, in terms of set theory, "infinite" is defined in terms of the very property that some people are finding so hard to swallow.

Grazza said:

Anyway, no one should be embarrassed about finding infinity a difficult concept - it's one of those things that seems to become more confusing the more you learn about it.

Not fit for human consumption!

Im with fraggle, grobbledegook and frederik.

EllipsusD said:

Perhaps, but I feel that you are wrong in assuming that infinite is a number at all.

I'm not. I was using (or at least intended to use) the term "infinite number" in an abstract, hypothetical sense.

not only are the lists of numbers infinite, but the difference between the amount of normal numbers and the amount of prime numbers is also infinate.

Yes, but you're forgetting that infinity + infinity = infinity. So there is no difference. The sets have the same size.

Infinity is not a number. An infinite number cannot be represented as a number, only as infinity itself.

Anyway, I really don't see the difference between infinity and eternity.

(Quasar not included :) )

bah, it's all equal to 42.

negative-infinty minus one

TeamKill said:

bah, it's all equal to 42.

Yes, and 3 is the Anti-Christ for keeping 2 and 4 apart and in the wrong order.

Yeah, and 4+2=6, and three 6s is the antichrist, too!

ravage said:

Anyway, I really don't see the difference between infinity and eternity.

Eternity is an infinite amount of TIME. Infinity is a very simple concept. An amount that is endless.

I AM A MORON I AM A MORON I AM A MORON I AM A MORON I AM A MORON I AM A MORON I AM A MORON I AM A MORON (t1meline) is infinity