Does infinity exist in the physical world?

[Upisoft]

Infinity is abstact concept, very useful in mathematics. Since the mathematics are some level of abstraction of the physical reality, I ask this question.

 

[Maynard Keenan]

Infinity is not some obscure, mythical concept. It is a simple mathematical concept.

 

[KTatis]

Uh good question I would say yes.

 

[Normal]

Infinity does exist, but it is so large that humans cannot truely understand it. We have to put up barriers on everything.

 

[Maynard Keenan]

Infinity is not always large. Sometimes is it small. Imagine the number .0000000... with infinite zeroes, but that is not the number zero. Infinitely small, but still substantial.

 

[MarcusHill]

It depends on what you mean by "infinity", "exist" and "the physical world". Sorry if that sounds like a coput, but I'm a mathematician.

Incidentally, a number smaller than any real number but not equal to zero is an "infinitessimal", not infinite. They're not really in vogue at the moment.

On a related note, 0.99999.... with infinitely many nines is equal to 1. Not slightly less, not "approaching", not subtly different from - they're two representations of the same number.

 

[yasic]

Infinity is not always large. Sometimes is it small. Imagine the number .0000000... with infinite zeroes, but that is not the number zero. Infinitely small, but still substantial.

Actually... it is zero.


Every real number has 2 infinite decimal expansions which equal the number. one of them ends with 0000... the other with 9999...

For example, take the number 12.4

The first infinite decimal expansion which equals 12.4 is 12.40000000... the second is 12.3999999999....


EDIT: Every real number except for 0 has 2 infinite decimal expansions.

EDIT2:

Gah I am making way to many mistakes here for a math major,

- Every real number without an infinite decimal expansion (except for zero) has 2 differently expressed numbers with infinite decimal expansions which are equivalent to the number. -

I really hope I did not miss anything this time *sigh*

 

[dud1]

Infinite zeros is just maths. Infinity cannot exist in the real world because it means 'without beginning or end'. If you say that God has always existed and always will then that is infinite. You can only say God is infinite in size if he is everything. That means God is all of us including atheists, Hitler, Stalin, Pol Pot and Satan too which since God made the universe you may agree with or not agree with.Take one away from infinity and it is no longer infinity.

 

[yasic]

Infinite zeros is just maths. Infinity cannot exist in the real world because it means 'without beginning or end'. If you say that God has always existed and always will then that is infinite. You can only say God is infinite in size if he is everything. That means God is all of us including atheists, Hitler, Stalin, Pol Pot and Satan too which since God made the universe you may agree with or not agree with.Take one away from infinity and it is no longer infinity.

Not quite

For instance, one could claim that there is an infinite number of distince points between any 2 given points (say the tip of your index finger and the tip of your thumb)

Mathematically, this is true, for our universe... well we don't know. For all we know, there might exist a smallest unit of space and a point as we know it does not exist, or any number of possibilities... we just don't know.

However, my personal feeling is that there IS an infinite number of points (in both space and time) between any point in space or time. That is why I chose the second option.



Also, one could claim that the universe has infinite length. As in it has no start or finish. We do not have any way to prove or disprove that at the moment either.

 

[Wiccan_Child]

I think it is likely that infinity does exist. If spacetime is hyperspherical (4D sphere), for example, then time and space are without end. There would be an infinite number of number of points between two arbitrarily selected points in spacetime (no typo; think sine), even if spacetime had a fundamental 'grainyness'.

 

[MarcusHill]

Take one away from infinity and it is no longer infinity.

That's exactly why I said it depends on your definition of "infinity". An infinite set is one whose elements can be put into a 1 to 1 mapping with those of any proper subset of itself. In other words, by definition, if you can't take one away from it without leaving the quantity unchanged, it isn't infinity. Not only that, but there are infinite numbers which are provably bigger than other infinite numbers.

 

[Wiccan_Child]

That's exactly why I said it depends on your definition of "infinity". An infinite set is one whose elements can be put into a 1 to 1 mapping with those of any proper subset of itself. In other words, by definition, if you can't take one away from it without leaving the quantity unchanged, it isn't infinity. Not only that, but there are infinite numbers which are provably bigger than other infinite numbers.

Plus you can't consider infinity to be a real number, and so arithmetic involving it (1 - ∞, for example) doesn't work. The same goes for division by zero (nullity?), and the square roots of -1 (i, -i).

 

[MarcusHill]

Plus you can't consider infinity to be a real number, and so arithmetic involving it (1 - ∞, for example) doesn't work. The same goes for division by zero (nullity?), and the square roots of -1 (i, -i).

Kind of. Division by zero is undefined, but there are arithmetics of both infinite numbers and complex numbers. They just don't work like the arithmetic of real numbers.

 

[Upisoft]

Incidentally, a number smaller than any real number but not equal to zero is an "infinitessimal", not infinite. They're not really in vogue at the moment.

You know there is no such number that is smaller than any real number. I thought you said you're mathematician...

 

[Eudaimonist]

Does infinity exist in the physical world?

I think it might be better to ask:

"Is there anything infinitely big or small, or countably infinite?"

Otherwise, the answer has to be: "Only as an abstract concept".


eudaimonia,

Mark

 

[MarcusHill]

You know there is no such number that is smaller than any real number. I thought you said you're mathematician...

That's why I said "they're not in vogue". They had to be posited and used in the early development of calculus, but even then mathematicians realised they weren't really a tenable concept. That's why there was a century of refinement in order to reformulate the foundations of calculus in terms of limits.

 

[RealSorceror]

The only thing that comes to mind is time. Other than that, I don't think infinity exists.

 

[Pesto]

Infinity is not always large. Sometimes is it small. Imagine the number .0000000... with infinite zeroes, but that is not the number zero. Infinitely small, but still substantial.

What you've said is mathematically impossible.

 

[Loudmouth]

From my reading, nature seems to abhor infinities as strongly as it abhors a vacuum. Plank time and Plank length, from my understanding, represent the smallest length and smallest time under which nature operates. The universe is also finite in mass, energy, and time as illustrated by Olber's paradox. Energy itself is released in quanta, not asymptotically smaller amounts that some graphs in classical physics indicate.

While you can construct mathematically consistent equations using abstract infinities, I can't think of one physical phenomena that is either infinite or truly asymptotic in nature.

 

[HumanisticJones]

Apart from the abstractions given, I'm leaning towards observable or inferable infinities being imposible. This doesn't mean that infinites cannot exist, but at any point that we observe something, we have inserted a destination (if infering from past evidence) or an origin (if observing from a given time). The mind would like to say that there cannot have been infinite time since we got to a point in time where we started looking back, but that is only because we observed our point on the line.

I don't know if I'm making sense with this or not, hopefully this is getting across.