How big is infinity?

[Smilin]

Originally posted by: Jeff7

Originally posted by: dejitaru

Its really big.

Too large, in fact, to be contained. So how can it exist?

Who says it needs to be contained? I wouldn't think that something infinite even could be contained.

It IS the container.

Our universe is merely a singularity that we exist within anyway. When people look around they tend to view the world that they see as the inside of a sphere that goes 360 degrees in any direction. In fact you are simply looking at a point. As you peer around you are seeing the point rotate, showing you different facets. We only *think* a point has no "directional facing" because it's infinitely small and that would be a correct assumption if you were viewing it from the outside.

 

[RACER]

my 2cents is that 0/0 or inf/inf is not undefined, but undeterminable.

It can be 0, 1, inf or undefined, therefore undeterminable.

 

[sao123]

Dont undeterminable and undefined mean the same thing?
They both mean that no set value has been established to represent this quantity or set.
Undefined is definately not the same as a NULL set.

 

[DOOPYLOOPY]

dejitaru has it on the head I think.

Infinity isn't a number. You don't have an infinite amount of objects u have the amount of objects is the set of infinity.

Infinity isn't so big it can't be contained that statement is completely stupid.

infinity just is.

and u can have a 1m interval and start at 0m if u go half that distance to 50cm and then keep going half the distance u will never reach the 1m. You can make n jumps and never reach 1m. { n : n is the set of all positive integers)

 

[Inspirer]

sorry for taking everybody back but,

Originally posted by: brjames

Originally posted by: Smilin

Originally posted by: dejitaru
1+1-1+1-1...=1+1-1+1-1...
so
1+(1-1)+(1-1)...=1+1+(-1+1)+(-1+1)...
simplified
1+(0)+(0)...=2+(0)+(0)...
therefore
1=2

Lol, you tard. you stuck an extra +1 in there.

See the ellipses? that means the series goes on forever... the proof is still fallacious but not cuz he "stuck an extra +1 in there"

Hazer beat me to it but I'll post it in my own words:

actually, it is because he stuck an extra 1 in there.
you can't write both series to the same distance without placing the "..." inside the brackets (which may be allowed, but it's ugly)

but most importantly, you can't have the "..." cancel each other out if both series aren't written to the same distance.

 

[JohnnyT]

This conversation thread is not infinitely long, but it felt like it at times. So here's a slight topic change:

The further we look back in space the further back in time we look. Doesn't that infer that if we had a large enough telescope, we could in ANY direction and see the universe as it was shortly after the big bang?

 

[Inspirer]

and then what ?

 

This is how i was taught infinity back in 6th grade (maybe seventh) in a proof logic and reasoning course:

First, imagine you have a hotel with one floor and infinitly many rooms. Now lets say you put people in every room. Now say five more people come in asking for rooms, what do you do? Tell everyone to move five rooms over. Now you ask, "But I thought every room was full!?!?!" My answer to you is, mention one person who cannot find a new room? The guy in room one will now be in room 6, they guy in room 100000000 will now be in room 100000005. Therefore infinity + x = infinity. Now to continue, lets say infinity people come to the door? Everyone cannot move down infinity rooms because they will be walking forever. What you do, right after your head explodes, is tell everybody to move over by their room number. There for, everybody still has a room, and there is now room for the new infinity people.
So ends my first situation.
Now for my second:
So long as you can match every number in one set with a number in the other set, there is an equal number of mebers, Correct? Now, make your integer set look like this: {0,-1,1,-2,2...} and your natural number set look like this: {1,2,3,4,5...} Quikly we can see that every integer is accounted for by every natural number so these sets are equal. What about rational numbers you say? well make your set look like this:
1/1 2/1 3/1...
1/2 2/2 3/2...
1/3 2/3 3/3...
. . .
. . .
. . .
Granted some numbers are repeated butthat would only make the set larger now smaller so i don't even bother thining of them. Now if we walk through this set making concentric square we once again have every number in the rational accounted for by naturals, and therefore the sets are equal. This is the smallest set of infinity hence its name aleph-not, the hebrew letter alef with a small zero to its lower right. Now natural numbers cannot be organized like this and are there fore a different level of infinity and are given the name aleph-one, you can guess the symbol. Past this I dont know, haven't taken calculus yet. But this is a good way to explain infinity in almost laymans terms.

BTW, this is my first post, if there is something fundamentally wrong in my manner of posting please tell me

 

[dejitaru]

and u can have a 1m interval and start at 0m if u go half that distance to 50cm and then keep going half the distance u will never reach the 1m. You can make n jumps and never reach 1m. { n : n is the set of all positive integers)

Unless n=infinity

Hazer beat me to it but I'll post it in my own words:
actually, it is because he stuck an extra 1 in there.
you can't write both series to the same distance without placing the "..." inside the brackets (which may be allowed, but it's ugly)
but most importantly, you can't have the "..." cancel each other out if both series aren't written to the same distance.

For the last time, there is no extra 1.
1+1-1+... goes on forever, so there are already an infinite number of ones. You can't add one to infinity, so that argument is null.

regarding:
1+1-1+...
If it ends in "+1", it will equal two. If it ends in "-1", it will equal 1. But it does not end. It has no value, may only be expressed as a formula.

 

[gururu]

this post is going on way too long, and gets more confusing.
you can't explain, describe, calculate, understand, or rationalize infinity.
you accept it.

 

Originally posted by: gururu
this post is going on way too long, and gets more confusing.
you can't explain, describe, calculate, understand, or rationalize infinity.
you accept it.

True, by its nature, infinity cannot be calculated or explained in true layman terms. But to say it can't be described or even UNDERSTOOD?!?! I tell you, never has the abstractness of something ever kept people from understanding it, even if it takes thousands of years. Infinity, being fundamentally numerical, is already easier to understand than say gravity which is purely intangable, which is described very easily and understood even easier. Granted explaining gravity and calculating it took time, it is definelty not impossible. If infinity were imposible to describe, there simply would be no word for it, for if it cannot be described, what use would one have for a word that no one knows?

Hotel Infinity, definetly the simplest way to describe infinity

If your confused take the time to read the short story above, I tried to sum it up earlier but either i did a bad job or people didn't want to read my rather long post. It is not difficult to conceptualize as it is written to teach younger people about infinity. I read a much better version four years ago, but I didn't feel like scanning it.

 

Originally posted by: JohnnyT
This conversation thread is not infinitely long, but it felt like it at times. So here's a slight topic change:

The further we look back in space the further back in time we look. Doesn't that infer that if we had a large enough telescope, we could in ANY direction and see the universe as it was shortly after the big bang?

I never understood why anyone could care less about what happened right after the big bang, please enlighten me.

 

[PIMPBOT5000]

WOW, didn't think it would be this popular!

 

[gururu]

JAGedlion, you can't compare the physical and hardly abstract phenomenon of gravity with the concept of infinity. Well, I guess you can since you did, but I disagree. I've thought enough of infinity to have once thought I understood it. But now I realize that it is truly an abstract concept; and truly abstract concepts can never be grasped. And so I realize that I have too often fooled myself in believing to have grasped it.
words cannot do it justice either. there just isn't enough of them or the time to say them.

 

[ynotravid]

Originally posted by: PIMPBOT5000
Ok, I was thinking about this a while back a never tried to get an answer to it so here go's...

On a number line there are an infinite amount of numbers...

There are also an infinite amount of prime numbers, however to a lesser degree of infinity when compared to the entire set of all integers. I have heard some say that since they are both infinitly large they are both equal amounts. However, since every number is not a prime number wouldn't that disprove the idea that they are equal?

I guess we're arguing over what equal means. If equal means "not better than" then probably infinity equals infinity. But if equal means "is exactly the same in every possible way" then probably there are different kinds of infinity.

 

[drag]

Infinity is a concept that means, beyond all possible measurement. Instead of saying "more then there could ever possible exist" when someone asks you a mathmatica question that is impossible to answer. Mathmatics is a construct of the human imagination, the human imagination does have limitations, there are somethings that mathmatics can never be used to explain, no matter how you twist it. The model is simply not perfect and can't at dealing with certain issues, so we have things like infinity to explain things math can't deal with.

How many numbers between 1 and 2? A math person could seem silly saying "well there is more numbers than there could ever possibly be", the person would just stare at him with a dumb look. So he just say "well it's infinite" and the guy would just nod and say "ah, infinite". Plus now they could put a nice sideways 8 instead of a bunch of question marks and phrases like "a undescribable large amount" out their formulas and make them look nice and important (not the math people the formulas, math people are very important)

Now a good discusion would be about the concept of having a number that equals "nothing of anything".
zero.

notice that in programming 0 = the first number of something and 1 equals the 2nd number of something, so go figure...

 

Originally posted by: ynotravid

Originally posted by: PIMPBOT5000
Ok, I was thinking about this a while back a never tried to get an answer to it so here go's...

On a number line there are an infinite amount of numbers...

There are also an infinite amount of prime numbers, however to a lesser degree of infinity when compared to the entire set of all integers. I have heard some say that since they are both infinitly large they are both equal amounts. However, since every number is not a prime number wouldn't that disprove the idea that they are equal?

I guess we're arguing over what equal means. If equal means "not better than" then probably infinity equals infinity. But if equal means "is exactly the same in every possible way" then probably there are different kinds of infinity.

There are very discrete levels of infinity they are called aleph-not, aleph-one, ect. I don't know how far it goes. Read my post above, it describes what it is to have equal and unequal infinities. The idea is that, sets have an equal number of members if for every member of one set, there is a member in the other. Therefore there are as many rational, integers, and naturals, but a different amount of irrationals and reals.

 

accidentally posted twice

 

[ynotravid]

Originally posted by: JAGedlion

Originally posted by: ynotravid

Originally posted by: PIMPBOT5000
Ok, I was thinking about this a while back a never tried to get an answer to it so here go's...

On a number line there are an infinite amount of numbers...

There are also an infinite amount of prime numbers, however to a lesser degree of infinity when compared to the entire set of all integers. I have heard some say that since they are both infinitly large they are both equal amounts. However, since every number is not a prime number wouldn't that disprove the idea that they are equal?

I guess we're arguing over what equal means. If equal means "not better than" then probably infinity equals infinity. But if equal means "is exactly the same in every possible way" then probably there are different kinds of infinity.

There are very discrete levels of infinity they are called aleph-not, aleph-one, ect. I don't know how far it goes. Read my post above, it describes what it is to have equal and unequal infinities. The idea is that, sets have an equal number of members if for every member of one set, there is a member in the other. Therefore there are as many rational, integers, and naturals, but a different amount of irrationals and reals.

I did read your post, and it was kinda late when I posted so forgive me, but the point I was making was even if you are to describe a perfectly legitimate means of defining equality, unless we all agree to use that definition for the discussion, we will can have multiple answers the original question that not only differ and cotradict, but are also correct.

 

Read the sites about Cantor, considering he invented it, I think we should ALL agree his way is the right way...:disgust:

P.S. Sorry, I'm editing this message, because i just re-read my last couple and feel I have been overly aggressive, and mean.

 

[ynotravid]

np

 

[drag]

It still doesn't make sense to me, how could have one infinity bigger then another? There both infinite, both beyond any possible any comprehention, so how could you mesure one to be more then another. I suppose you could say there was more then one way to reach infinity, there is probably a infinites way to reach infinity, but since by definition it is actually impossible to reach a infinate number, it is then a non-issue.

It's like saying zero divided by 24 is a smaller zero than a zero divided by five.

Is it possible to say 2(infinity) > infinity... I don't think so.

 

[RossGr]

Drag,
Strange but ture, There are indeed different "sizes" of infinity. This is all from set theory, take a set, form all possible subset, the set of all subsets is necessarily larger then the original set. So if you form all possible subsets of the integers you have the real numbers, clearly the set of all possible subsets is a larger set, therefore there are more real numbers then integers. There are an infinite number of integers and there is an infinite number of Real numbers, but the CARDINALITY of the Reals in larger then the CARDINALITY of the integers.

This is all well understood stuff, if you wish to learn the details you need a good course in Set Theory.

Are you the same Drag as in PF?

aka Integral

 

[Inspirer]

Originally posted by: JAGedlion

There are very discrete levels of infinity they are called aleph-not, aleph-one, ect. I don't know how far it goes. Read my post above, it describes what it is to have equal and unequal infinities. The idea is that, sets have an equal number of members if for every member of one set, there is a member in the other. Therefore there are as many rational, integers, and naturals, but a different amount of irrationals and reals.

I was told that it was proven that there's an infinite number of alephs (infinite number of infinitys)

 

[Inspirer]

Originally posted by: dejitaru

Hazer beat me to it but I'll post it in my own words:
actually, it is because he stuck an extra 1 in there.
you can't write both series to the same distance without placing the "..." inside the brackets (which may be allowed, but it's ugly)
but most importantly, you can't have the "..." cancel each other out if both series aren't written to the same distance.

For the last time, there is no extra 1.
1+1-1+... goes on forever, so there are already an infinite number of ones. You can't add one to infinity, so that argument is null.

regarding:
1+1-1+...
If it ends in "+1", it will equal two. If it ends in "-1", it will equal 1. But it does not end. It has no value, may only be expressed as a formula.

I realize that the "added" 1 came from the continuation of the series
what I'm saying is that even if there are infinite one's, you're not allowed to write a different portion of the series on either side of the equasion and have the unwritten (...) portions of the series' cancel each other out !!!