Infinity
- Thread starter Lithp
- Start date
This does not make sense. Could you elaborate? Besides, which infinity are you talking about, there are several orders of infinity, and they are not the same. Thus, a set of all integers is a lower order of infinity, a set of all real numbers is a higher order of infinity.
Anything that can be numbered If you can conceive that there is an infinite amount of them. It could be integers, kilometers, steps. The first integer before an infinite number of integers is 1; the last integer before an infinite number of integers is 1. Step number 1 is the first step of an infinite number of steps; step number 1 is the last of an infinite number of steps, and so forth.
That doesn't really make it any clearer, and still doesn't make sense to me. "Step number 1 is the last of an infinite number of steps" is just wrong. Where does step 2 fit into this, and step 3, 4, 5...? I presume since you put this into Spirituality and Philosophy that you're not interested in a discussion of what infinity means mathematically, which is too bad, there are some interesting insights to be had there, that SJP hinted at. The infinity of real numbers, for instance, is infinitely larger than the infinity of integers, in fact there are infinitely more real numbers between any pair of integers than there are integers, a surprising fact that's remarkably easy to prove and you don't have to be a mathematician to understand it.
What are *YOU* talking about?
What are *YOU* talking about?
Zero's just the first integer in a sense, though it has some special properties no other integer has and some people will argue on that basis that it's not an integer, it's in a class by itself. You can't divide anything by zero, for instance. Zero's a pretty interesting and useful concept, just like infinity. Lots of numbers are like that, like pi and epsilon, they show up in all sorts of unexpected places. Pi, 3.1415926... is just the ratio of a circle's circumference to its diameter, a fairly simple idea in principle, and epsilon, 2.71828... is the base of what's called natural or Naperian logarithms, a number that emerges from an analysis of compound growth rates. They show up all over the place in mathematical physics in situations that have nothing to do with circles or growth rates.
Yes, I'm a math and numbers geek.
Yes, I'm a math and numbers geek.
That doesn't really make it any clearer, and still doesn't make sense to me.
Quite so, Dexter. It sounds more like mysticism than mathematics. Besides, it is not clear which infinity he is talking about. There are literally infinite orders of infinity (Aleph Null, Aleph One, Aleph Two etc.).
It sounds like he is talking of Aleph Null, but I don’t know. Lithp, could you give a web link to what you are talking about?
Incidentally, zero was discovered by ancient Hindus. I don't think ancient Romans had a concept of zero (there is no zero in Roman numerals).
Quite so, Dexter. It sounds more like mysticism than mathematics. Besides, it is not clear which infinity he is talking about. There are literally infinite orders of infinity (Aleph Null, Aleph One, Aleph Two etc.).
It sounds like he is talking of Aleph Null, but I don’t know. Lithp, could you give a web link to what you are talking about?
Incidentally, zero was discovered by ancient Hindus. I don't think ancient Romans had a concept of zero (there is no zero in Roman numerals).
Nope, sorry, can't do it that way. :smile: Euclid was quite clear about that: parallel lines won't meet at any point no matter how long you make them. He didn't use the word infinity in his fifth postulate, he said something like "lines produced indefinitely far..." But there are non-Euclidean geometries too, in which parallel lines meet at a finite distance, or get farther apart. Depends on the nature of the curvature of the surface the lines are drawn on.
I can't argue that:smile: a lonnnng long time ago in a geometry class in college a professor did show us how they meet but I can't remember the concept.....I guess it wasn't something important to me ....:lol:
Sorry, I wasn't sure where to post this. Sorry as well for the confusion. Perhaps I can explain it this way (you guys can tell me if it makes sense):
If you can imagine the theory that "an object in motion stays in motion unless acted upon by some other force..." and that you were to push an object away from you in such an environment that offered no resistance or force whatsoever, then that object would travel an infinite distance. The number of pushes required for this infinite journey would be one. This would be the first and the last number of pushes required.
The same can be true when counting; If I were to start counting to infinity (and by counting I mean in a very elemental sense: 1,2,3,4, etc.) 1 would be the first number towards the journey to infinity, One would also be the last number towards the journey to infinity.
I guess what I am proposing is that a journey to infinity begins and ends with 1 because all other numbers after that are "this infinity" of which I speak. This is what I meant when I said step number one is the first and the last step towards an infinite number of steps.
As for zero, the same would hold true for -1. Zero is the starting point of the journey to infinity involving negative numbers -1, -2, -3, etc.
If you can imagine the theory that "an object in motion stays in motion unless acted upon by some other force..." and that you were to push an object away from you in such an environment that offered no resistance or force whatsoever, then that object would travel an infinite distance. The number of pushes required for this infinite journey would be one. This would be the first and the last number of pushes required.
The same can be true when counting; If I were to start counting to infinity (and by counting I mean in a very elemental sense: 1,2,3,4, etc.) 1 would be the first number towards the journey to infinity, One would also be the last number towards the journey to infinity.
I guess what I am proposing is that a journey to infinity begins and ends with 1 because all other numbers after that are "this infinity" of which I speak. This is what I meant when I said step number one is the first and the last step towards an infinite number of steps.
As for zero, the same would hold true for -1. Zero is the starting point of the journey to infinity involving negative numbers -1, -2, -3, etc.
The important thing to remember is that infinity is not a number; it is a concept.
Infinite means "without end". "in"= without or lacking. "fine"= end, finish.
Technically a thing is not truly infinite if it has a beginning, for then it has an "end", its beginning. However, there is often talk about something which begins and then lasts until infinity. Then again, there is nothing in science that supports such an idea.
Quantum loop gravity theory does espouse a particular facet of infinity, that matter that constitutes the universe has always existed and will always exist. This same theory goes beyond before the Big Bang and states that the matter which is our universe now existed before the Big Bang as a universe that was undergoing Universal Contraction, as opposed to Universal Expansion which we experience now.
Another definition or understanding of infinite is that something as simple a baseball cover can be considered infinite; specifically without end. If you were an ant crawling on the surface of a baseball, you would never encounter the end of the surface. Eventually it might dawn on you that you've been some place on the ball as before; but it certainly would be difficult to understand how it could be that you could end up where you started without turning around.
As stated at the beginning of this answer, infinity is not a number; therefore one cannot calculate with it. I say this even though "infinity" is mentioned several times in relation to mathematics. However, it is never properly utilized as a number; for it does not follow the laws that all numbers (counting, whole, real, positive, negative, irrational, and even imaginary numbers) do follow.
And since you are asking this in Astronomy & Space, a common question is whether our universe is infinite. The answer is: even though the universe is very large and even though one cannot reach its end (making it technically infinite), our universe is finite.
On the other hand, the super-universe in which our universe exists is literally infinite.
Infinite means "without end". "in"= without or lacking. "fine"= end, finish.
Technically a thing is not truly infinite if it has a beginning, for then it has an "end", its beginning. However, there is often talk about something which begins and then lasts until infinity. Then again, there is nothing in science that supports such an idea.
Quantum loop gravity theory does espouse a particular facet of infinity, that matter that constitutes the universe has always existed and will always exist. This same theory goes beyond before the Big Bang and states that the matter which is our universe now existed before the Big Bang as a universe that was undergoing Universal Contraction, as opposed to Universal Expansion which we experience now.
Another definition or understanding of infinite is that something as simple a baseball cover can be considered infinite; specifically without end. If you were an ant crawling on the surface of a baseball, you would never encounter the end of the surface. Eventually it might dawn on you that you've been some place on the ball as before; but it certainly would be difficult to understand how it could be that you could end up where you started without turning around.
As stated at the beginning of this answer, infinity is not a number; therefore one cannot calculate with it. I say this even though "infinity" is mentioned several times in relation to mathematics. However, it is never properly utilized as a number; for it does not follow the laws that all numbers (counting, whole, real, positive, negative, irrational, and even imaginary numbers) do follow.
And since you are asking this in Astronomy & Space, a common question is whether our universe is infinite. The answer is: even though the universe is very large and even though one cannot reach its end (making it technically infinite), our universe is finite.
On the other hand, the super-universe in which our universe exists is literally infinite.
Okay, you're talking about the infinity of integers, aleph null, and you're right that 1 is the first number on the way, but it's not the last one. First, it can't be if there's a number after it, and there is. In fact there's an infinite number of numbers after it. Second, there really is no last number in counting to infinity, there's no number that's one less than infinity, or two less than infinity, etc. That's what infinity means and, as Socrates pointed out, it's not a number. Certain mathematical operations are permitted with it, but you can't count up to it and you can't use it in ordinary arithmetical calculations. If we say, for instance, that 1 divided by infinity is zero, which seems superficially logical, then by the rules of arithmetic zero times infinity must be 1. But then 2 divided by infinity is also zero, so zero times infinity must be 2. By extending that, you can see that zero times infinity can be any number at all, so division by infinity becomes an undefinable operation. The mathematicians dodge it by saying the value of the quotient n/x, where n can be any number, tends toward zero as x increases without limit. To engineers, who often don't have a lot of patience with such mathematical formalism, that's usually enough to justify throwing such terms out of a calculation as being insignificant.
Not really, "finite but unbounded" is the proper description.
Well... we don't really know that, it's just speculation. It does emerge as a possibility in the equations of various attempts to reconcile general relativity and quantum mechanics, like loop quantum gravity and string theory, but we don't have the data that would justify such a conclusion. Our universe may be finite but unbounded, it may be infinite and boundless, it may be one of approximately 10^500 universes with different laws of physics existing as bubbles in a megaverse... Fascinating speculations, but there's no data.
No, I don't think I'd buy that, Spade, what cosmologists think about at least has roots in some sort of sandy reality, while mystics have no contact with reality at all in my distinctly unhumble opinion. I would, however, immediately agree that the fringes of contemporary physics are pretty far out there in the realm of so far unsupportable speculation. Some really elegant and lovely mathematics, which has a certain value on its own, but so far it doesn't predict anything testable that the conventional wisdom doesn't also predict. But that's always the case when new theories are developing.
I don't agree mystics have no contact with reality. Mystics simply have a different interpretation and mode of response to reality. Science is objective while mysticism is subjective.
It's not objective to deny the reality of subjective thought.
Yes, I know you think that way. I think mysticism is nonsense, and has no value at all. It's misleading, deceptive, and incoherent. Subjectivism and mysticism aren't the same thing.
You are right, subjective thought is very real. However, it is also meaningless. A subjective thought is resident only in the mind of one individual, it has no applicability to anybody else.
Suppose I say ‘I like vanilla ice cream’. That is subjective thought. But that means nothing to others. To you, it is just a curiosity, nothing more.
So subjective thought is meaningless, of little value, unless it can be converted into an objective thought.