What if objects go toward each other rather than away

[Skhandelwal]

If we all objects for some reason stop, then by gravity, they will all start submerging w/ each other. Well, what I was wondering is that if that happens, would it be satisfied when everything becomes one, or would it start getting more and more dense till it can't get dense anymore and then big bang? If big bang, then how do you tell what is the limit?

 

[Danger]

Hi, Skhandelwal. It's a bit hard to understand your exact question. If the mass of the universe is sufficient to overcome the expansion, then eventually that expansion will reverse and everything will converge to a single point usually referred to as 'The Big Crunch'. That would be a black hole, from which a new 'Big Bang' might create a totally different universe. I don't know what your last sentence means.

 

[Skhandelwal]

Don't worry about it, but how big is a point? And why would it turn into a black hole? I mean objects just colliding together would start a nuclear reaction and they would all begin to form a big sphere but when that star dies, ooh, I get it.

 

[Danger]

A point is a point in the mathematical sense of the term; it has no dimensions. That is the basis of a singularity. It has a certain amount of mass, such as the original star, but it is compressed to zero volume which therefore gives it infinite density. Because of the inverse square law of gravity, at some point along the way that density gives an escape speed equal to or greater than the speed of light. At that stage, it officially becomes a black hole.

 

[Skhandelwal]

1. Wait, if points have no volume then how can an infinite sum of them make it? If points have no dimensions then how come infinite sum o them make up a line? I mean 0timesinfinity is still going to be zero.

2. Btw, if let's say 2 grams is compressed to zero volume, it gives infinite density, and if 2 billion grams are compressed to zero volume, which would also give infinite density, would 1 infinity greater than another?

 

[DaveC426913]

This is why you don't do math with infinities.

 

[Mk]

You know the different sets of numbers? As in naturals, reals, irrational, complex? Infinity does not "mix."

 

[Skhandelwal]

But I thought you guys understand infinity, what you guys just said indicates that there is a lot more to understand about it than we have understood.

 

[ZapperZ]

1. Wait, if points have no volume then how can an infinite sum of them make it? If points have no dimensions then how come infinite sum o them make up a line? I mean 0timesinfinity is still going to be zero.

You need to learn a bit of mathematics here before making statements like that. For example, I can easily write what you call "0 times infinity" as "0 times 1/0". This means that what I have as "0 times infinity" is equal to 0/0. In mathematics, this is undefined! It totally depends on that kind of expression one is using to arrive at such a thing. If I have, for example sin(x)/x, where x approaches 0, then do you think I have 0 when x=0?

When arguing something based on mathematics, one truly needs to understand the mathematical rules. There are HUGE areas of mathematics that deal with the handling of "infinities". One only needs to take a class in complex algebra to realize this.

Zz.

 

[Skhandelwal]

Well I am taking AP calc in high school which makes me a college level mathematician, so I thought I was good enough. Sorry, btw, I didn't know that infinity equals underfined as you simply replaced infinity by 1/0. How do you figure that?

 

[russ_watters]

Ehh - school just started a few weeks ago, didn't it? In a few more weeks, the answers to your questions here will start making a lot more sense...

 

[monkeykoder]

I can't wait till you see L' Hospital's rule it is a real mind bender when you first see it.
P.S. AP Calculus isn't necessarily equivalent to college calculus I have known many people who couldn't get into college calculus who had passed AP calculus with a 5 on the AP test.

 

[Skhandelwal]

what what what! Dude, that was probably because they didn't pass the proficiency exam.

About the 1/0, I get it, since undefined means infinity in terms of secant lines. But what I still don't get is that if points have no dimensions? How can they exist on a dimensional coordinate system? And how can they make up a line? As I progress to take calculus, would I get answers to these questions or we don't have it?

 

[selfAdjoint]

what what what! Dude, that was probably because they didn't pass the proficiency exam.

About the 1/0, I get it, since undefined means infinity in terms of secant lines. But what I still don't get is that if points have no dimensions? How can they exist on a dimensional coordinate system? And how can they make up a line? As I progress to take calculus, would I get answers to these questions or we don't have it?

Well you won't learn that in intro calculus. That issue is part of measure theory, which is taught in college upper division and graduate courses with titles like Real Analysis. you might look at measure theory on wiki and see what you make of it, and we do have several math forums here which could be of help to you.

 

[Skhandelwal]

Could you point out a specific course which I could take to get these questions answered or would I have to major in certain part of math?