What Is Infinity? Explained for Beginners

[Snitz]

Hello,

Please excuse me if I may sound an ignorant compared to all of you, but I was always stupid and never paid attention to any of my physics classes and now I feel so stupid for missing on the most important subject of our lives and our universe.

I was discussing a notion with a friend of mine 2 days ago, it's kind of a theory, I still don't know if it's new so I'm still writing an article about it.

But I would like to know what is infinity?
Does it have a fixed explanation or does it vary from one person to another?
And is our universe infinite?
I'd say no, if I'm wrong please correct me with a detailed explanation that I would be able to understand.

Thanks!

 

[Snitz]

I think I got my answer from this article here:
http://map.gsfc.nasa.gov/m_uni/uni_101shape.html

It proves that the universe is not infinite as most people think, it's still expanding to a number and a time we don't know.
And someday (maybe in a zillion years) it will stop expanding and collapse, just like the article says.

Please, correct me if I'm wrong!

 

[daniel_i_l]

1) A set of numbers is infinate if it has no defined end (or upperbound). So the volume of the universe is infinate if there's no upperbound to its volume.
2)Nobody knows if the universe is infinate or finate in volume.

 

[arunma]

Infinity isn't really a thing in its own right. It's merely a mathematical concept that physicists often find helpful. Often times a system will behave in a way such that as time increases, it tends toward some particular behavior, and we like to call this the behavior of the system at infinite time. Or sometimes we will measure potential differences (voltages) with respect to infinity. In this case, infinity just refers to a really, really long distance. When discussing the optics of refracting lenses, we often talk about viewing objects that are located "at infinity." In this case, that can mean as little as 20 feet or so away. Mathematically, when we talk about the behavior of a function as its variable goes to infinity, we're talking about the functions behavior as its variable increases without bound.

Now as to the size of the universe, most people these days would agree that it is probably not infinite in size. In fact there are estimates on the mass of the universe. It's big, but not quite as big as we once thought.

 

[billiards]

Infinity is as large a number as could possibly be conceived, doubled, tripled, and then some.

 

[daniel_i_l]

Infinity is as large a number as could possibly be conceived, doubled, tripled, and then some.

That is wrong. Infinity isn't a number, it's a quality of a set of numbers. Let's say you look at the set of all integers. Every integer is finate but the set of integers is infinate because you can't point to a certain number and say "this is the end of the last integer". And in terms of distances, it means the same thing, that there's no distance for which you can say "it's no further than that"

 

[rbj]

1) So the volume of the universe is infinate if there's no upperbound to its volume.
2)Nobody knows if the universe is infinate or finate in volume.

i do not think that is true (but would be happy to be corrected).

i think, at present, a reasonalbe upper bound on the volume of the universe is in the order of magnitude ((14 billion years) x c)³ .

it's not as if there was this empty infinite volume of space that the big bang occurred in. space, itself, had been expanding along with the stuff inside since the big bang. i don't think there is this empty volume of space outside of the visible universe. at least not an infinite sized empty volume of space.

 

[daniel_i_l]

The universe can have:
1) Started out uniformly dense
2) Be expanding
3) Have an infinate volume
For example, the universe could have started out with an infinate volume and with matter distributed uniformly. It would have started out being very desne which means that there was very little distance between the matter:

... ->
... ->
... ->
| | | |
\/\/\/\/

Then the universe started expanding which means that the average distance between the matter started getting bigger:

.  .  .  . ->
.  .  .  . ->
.  .  .  . ->
|  | | | 
\/\/\/\/

 

[billiards]

That is wrong. Infinity isn't a number, it's a quality of a set of numbers. Let's say you look at the set of all integers. Every integer is finate but the set of integers is infinate because you can't point to a certain number and say "this is the end of the last integer". And in terms of distances, it means the same thing, that there's no distance for which you can say "it's no further than that"

My point was not that infinity is an actual (nameable) number, but that it is immeasurably large. By the way infinite is spealt with an 'i' ;).

 

[russ_watters]

Hello,

Please excuse me if I may sound an ignorant compared to all of you, but I was always stupid and never paid attention to any of my physics classes and now I feel so stupid for missing on the most important subject of our lives and our universe.

I was discussing a notion with a friend of mine 2 days ago, it's kind of a theory, I still don't know if it's new so I'm still writing an article about it.

But I would like to know what is infinity?
Does it have a fixed explanation or does it vary from one person to another?
And is our universe infinite?
I'd say no, if I'm wrong please correct me with a detailed explanation that I would be able to understand.

Thanks!

Oy! There is so much wrong with this post, it is scary. Others have explained infinity, so I'll make an attempt to tackle the rest.

Your concept of knowledge itself is flawed.

-You can't figure out science on your own: you need to drop that idea. Writing an article is an utterly useless exercise with the level of knowledge you have. Ie...
-You don't understand what science is, so you can't possibly come up with a new idea about it. Ie...
-In science (math, actually, here), definitions are unequivocable. They have to be, otherwise it would be impossible to convey ideas. For the most part, language in general has to have unequivocable definitions, otherwise people wouldn't really be speaking the same language even if they thought they were.
-You answered "no" to a question that didn't have a yes or no answer...

Sorry if this sounds harsh, but you are going down the wrong path and need to change that. If you don't know something, don't speculate idly about it, just look it up or ask about it.

 

[DyslexicHobo]

I liked this explanation of the term "infinity":

A number which you can choose any number s, so that s+1 is always smaller than infinity

 

[u83rn00b]

infinaty is a number or something that never stops growing, it keeps going on ansd on forever and ever. Space is sooo huge it is currenly impossibal to tell if it is infinate or like san andres it jus like stops or something. It is know tho that there are hundreds possibaly millions or trillions of galaxies. Sine there are so many galaxies, i wonder if in some of those there are other lifeforms which are like us but different. It is possibal tho...

 

[Snitz]

Oy! There is so much wrong with this post, it is scary. Others have explained infinity, so I'll make an attempt to tackle the rest.

Your concept of knowledge itself is flawed.

-You can't figure out science on your own: you need to drop that idea. Writing an article is an utterly useless exercise with the level of knowledge you have. Ie...
-You don't understand what science is, so you can't possibly come up with a new idea about it. Ie...
-In science (math, actually, here), definitions are unequivocable. They have to be, otherwise it would be impossible to convey ideas. For the most part, language in general has to have unequivocable definitions, otherwise people wouldn't really be speaking the same language even if they thought they were.
-You answered "no" to a question that didn't have a yes or no answer...

Sorry if this sounds harsh, but you are going down the wrong path and need to change that. If you don't know something, don't speculate idly about it, just look it up or ask about it.

Don't get me wrong, I totally agree with you.
I have nothing to do with science, that's why I feel so useless right now.
But this theory of mine is more philosophical rather than scientific. However, it has a very small scientific part.
That's why I wanted to make sure of this particular answer before I proceed and it turned about that I was right.
Thank you for clearing up the answer.

 

[rcgldr]

what is infinity

There's always wiki:

http://en.wikipedia.org/wiki/Infinity

In the case of an unbounded line, infinity is used to designate the imaginary ends of a line that really doesn't have ends.

In the case of sets, infinity means that the number of elements isn't finite.

In the case of calculus, infinity is often used to describe the limit of something approaching an unbounded case.

 

[M Grandin]

When I was a young boy about 10 years old, I often imagined an infinate long
fence while gone to bed for sleep. Trying imagining this made me feel ill -
as I realized what it meant - a sort of mental impossibility. But one day,
still that young boy, I looked at a "circular" fence around a flower-bed outside
a food-shop. There was my endless fence, I thought - one could endlessly
run along that fence. I was proud of this "discovery" - remember I was a young boy and had never heard the concept "infinity" being discussed.

An interesting (coincidence?) thing is, that the symbol for that food-shop
market concern later became the sign for "infinity" (a lying "8") - one of the
more strange things I have experienced in life.

 

[Crosson]

Most people have infinite confused with indefinite.

A set X is infinite if for each positive integer n, there is a subset of X with n elements.

Even better, a set X is infinite if it can be put into one-to-one correspondence with a smaller subset of itself.

i think, at present, a reasonalbe upper bound on the volume of the universe is in the order of magnitude ((14 billion years) x c)3 .

it's not as if there was this empty infinite volume of space that the big bang occurred in. space, itself, had been expanding along with the stuff inside since the big bang. i don't think there is this empty volume of space outside of the visible universe. at least not an infinite sized empty volume of space.

The upperbound you gave is correct for the visible universe. But according to inflation theory, there was a time when the universe expanded much faster then SoL, which is why the visible universe is not unambiguously "the universe". Cosmologist generally make claims about the visible universe, it is not know whether the universe as a whole is much larger or even unbounded.

 

[prasannapakkiam]

INFINITY = a/0

 

[Crosson]

INFINITY = a/0

This is nonsense.

 

[prasannapakkiam]

Really?
Consider y=1/x
find x when y=0
therefore: x=1/0.
Now anyone can see that this curve cannot touch the x-axis unless the value of x is infinitely large- i.e. infinity
therefore INFINITY=x/0=a/0

A simple example: In calculus:
IMPROPER INTEGRALS

Integral INFINITY, 1(1/x^2)
=-1/x|INFINITY, 1
=-1/INFINITY--1/1
=1 ==>
why is 1/INFINITY = 0?
substitute a/0 into 1/INFINITY.
therefore: 1/INFINITY = 0/(a*1)
= 0-->

 

[Gib Z]

No. It is nonsense. Perhaps you should brush up on your calculus, an Improper Integral is one in which the function being integrated diverges within the specified limts, eg $\int^1_{-1} \frac{1}{x} dx$, or where one or two of the bounds approach +/- Infinity eg $\int^{\infty}_0 \sin x dx$.

Your integral, $$\int^{\infty}_1 \frac{1}{x^2} dx$$, when dealt with rigorously, makes no sense at all. That integral is only given meaning when written as it is meant to be,

$$\lim_{a\to \infty} \int^a_1 \frac{1}{x^2} dx = \lim_{a\to \infty} (\frac{-1}{a} - \frac{-1}{1}) = 1$$.

So as we can see, what you really mean was $a/x \to \infty$ as x approaches zero.

EDIT: A much easier method of seeing why your definition is non sense is because it implies all numbers are equal.

 

[prasannapakkiam]

Note: I only taught myself calculus for my hobby purposes of Game Programming. Anyway, I shall never come back to this thread if you can answer my question:

1/0 and 2/0
which is greater?

 

[Gib Z]

Neither of the 2 are even defined. The fraction can not have a denominator of zero. In fact, by your reasoning since a/0 = infinity, then a=0*infinity, which implies we get the same result no matter what a is, meaning all numbers are equal! So you must think they are equal, which they are not! Only if we took limits as the denominator approached zero they would be equal.

 

[prasannapakkiam]

okay fine...

 

[FrogPad]

Note: I only taught myself calculus for my hobby purposes of Game Programming. Anyway, I shall never come back to this thread if you can answer my question:

1/0 and 2/0
which is greater?

thanks for the laugh :)

I seriously needed that. Finals are getting to me.

 

[jackiefrost]

Heck, I can tell you WHERE infinity is
It's the place where you go to get charges when you want to move them from a place of absolute zero potential.

[Just kidding... :tongue2:]

 

[IMP]

It is the luxury car division of Nissan Motor Corp. I win...:rofl:

 

[Siggi]

There is no such thing as 'infinity', beyond an abstract mathematical concept that has no meaning in 'reality'.

 

[CRGreathouse]

There is no such thing as 'infinity', beyond an abstract mathematical concept that has no meaning in 'reality'.

Don't foist that term on us. We mathematicians don't claim "infinity" as one of our own -- we have a number of different concepts of infinite for various fields, but no overarching singular noun "infinity".

 

[tommyburgey]

Is is right to say that infinity is the number of straight lines in a circle's circumference, infinity + 1 is just increasing the circle's circumference by one (or radius?)?

 

[matt grime]

Is is right to say that infinity is the number of straight lines in a circle's circumference

No, it is not right. It doesn't make sense at all as a definition for anything.

 

[Siggi]

Don't foist that term on us. We mathematicians don't claim "infinity" as one of our own -- we have a number of different concepts of infinite for various fields, but no overarching singular noun "infinity".

Whether or not you 'claim' it is irrelevant, the only place it's postulated is in the field of maths, but is meaningless none the less. Somebody's attempt to lend it credence I expect. ;)

 

[Dragonfall]

Don't forget, the universe might be compact!

 

[Idjot]

In the fictional words of Leto II in the book; God Emperor of Dune, by Frank Herbert: "No infinity exists to be demonstrated"

The word "infinite" is like the integer "0".

"0" represents "no beginning" and "infinite" represents "no end"

They are essentially the same no-thing.

The true meanings of "0" and "infinite" are akin to anti-matter in our minds. They could not exist without destroying us first, which would not allow us to understand because we'd be dead! In the anti-world, "1" and "finite" are switched with "0" and "infinite"
in this paragraph.

 

[Hurkyl]

I see no reason to allow this to continue. If you actually want to argue for a philosophical position, then start a thread to do so. (And do it in the philosophy of mathematics forum)