Infinately Interesting

[Gen-X]

Sam... I know you are going to love this one.
(So I am going to ask for your help and input here).

I was reading this book and it was talking about infinities and how they are not equal to each other.


Lets take infinite :

1 + 2 + 3 + 4 + 5 + 6 + ...... infinity

Now lets take 2 x infinity :

2 x ( 1 + 2 + 3 + 4 + 5 + 6 + .... infinity)

OR

2.1 + 2.2 + 2.3 + 2.4 + 2.5 + 2.6 + ....

which leaves us :

2 + 4 + 6 + 8 + 10 + 12 + ....


Here is the interesting thing. If the second infinity is only the sum of every SECOND number (ie no odd numbers) then isn't it only HALF as big as the first infinity which contains EVERY number?

So doesn't that mean :



infinity
-------- = 2
2 x infinity



and NOT a 1/2? or even infinity?


I know its mathematical so I don't know what relevance it has in our real world (I just had to add that Sam).... Maybe if we one day FIND an infinity in our universe (and how would we know the end isn't just around the next corner) how do we know they actually exist in the real world?

I just found the maths interesting :D

[Edited by Gen-X on 05-26-2000 at 12:05 AM]

Infinity is defined as having no limits, no ends, to continue for ever...therefore regardless of even/odd numbers or any other attempt to measure or defined Infinity by mathmatics does not nake sense either theoritically or practicularly.

Infinity is not a measurement, it is a magnitude...

Arguing about the mathmatical possibilities of Infinity are the same as the philosophical arguements regarding will the sun rise tommorrow, or the sporting agreements regarding whether Port Adelaide can win the AFL.....sorry off the point there.

[Sam Finch]

hehe, the answer's a half :D

something like this you can answer quite easily if you think of it in terms of limits, we have 2 sequences of numbers which we're adding up, the first one is

N(N + 1)
1 + 2 + 3 + ......... + N = ---------
2


2 + 4 + 6 + ......... + 2N = N(N+1)

therefore

N(N + 1)
X = ---------
2N(N + 1)



X is your infinite sum BTW, all we have to do to evaluate our sum when N is set to infinity, but before we do this we can cancel some of the Ns out,


N(N + 1)
X = ---------
2N(N + 1)

N
= ---------
2N

1
= ---------
2


doing things like that does have applications in the real world, usually evaluating things when N = 0 and you have to calculate something divided by N, you have to do some rearanging to see if you can get the N off the bottom before you can evaluate it, if it won't come off the bottom then the answer's infinity.

you do have to accept that the number of terms in both series are equal, and you will object to it but they are in fact equal.


Enjoy your book :D

There is no such number as infinity. Infinity is non-ending.

[code][b]
Infinity + Infinity = Infinity

Infinity - Infinity = Infinity

Infinity x Infinity = Infinity

Infinity
--------- = Infinity
Infinity

[kedaman]

Compare infinity to "null"

10+null=null
3*null=null
null-null=null
null*null=null

That's just what I saying. Sorry Sam, but there is no 1/2 of infinity or 2(infinity). Just infinity,

[kedaman]

I agree Meg,
Just like null is "no valid data"
Infinity is "no valid number"

[Sam Finch]

did I say there was 1/2 of infinity? no, some infinities are bigger than others though.

you can do maths with infinity so long as you treat it like a normal number until you evaluate it, alot of the time you can get the infinity out

[kedaman]

Reminds me of complex values

If you mean this:

n * 2 = 2n

Yes we can have that, nbut you can not have

infinity * 2 = 2(infinity)

You cannot have twice as much as something that never ends.

[kedaman]

Null can't be a value, infinity also isn't a specific value

[Gen-X]

I thought they would all love that :D

And doesn't it just show how as finite, limited human beings we simply cannot grasp nor understand the concept of "infinity".

No body on the face of the earth or who has ever lived on it has ever seen an "infinity"... because in order to have seen it you have to acutally BE it and in order to BE it you would not be a "finite, limited human".

So it cancels itself out.


Oh and Sam... this is a perfect example of maths and the real world diverging greatly. As far as we know infinities don't exist... yet maths not only shows they exist but that they can come in different shapes and sizes.

Everyone took the piece of information to be true they wanted to... the Mathematician took the maths... the realists took the limitless infinity...

Perhaps one day when we can BOTH look at it without either of these 2 concepts we might actually get somewhere.

[kedaman]

Perhaps we could just leave infinity. Then we actually would get somewhere

No body on the face of the earth or who has ever lived on it has ever seen an "infinity"... because in order to have
seen it you have to acutally BE it and in order to BE it you would not be a "finite, limited human".

Wedon't have to be infinit. Look at maths for example.

[Gen-X]

Yes, lets look at maths...

So has anyone "seen" an infinity? Or have they just "contemplated" it?

1 + 2 + 3 + 4 + 5 + .....

Now I can say that is infinity but I haven't acutally added them up... I can do approximations and I can do all of these mathematical derivations....

But does that mean I have actually "seen" an infinity? Have I actually observed it? Or just mathematical formulas that relate to it?

Can anyone NAME an infinity that exists in our universe?

[noone]

Isnt the universe itself infinite? Expanding without borders...

[Gen-X]

Isn't the Universe Infinate? Expanding without borders?


That brings up so many questions :

1. Has anyone SEEN the end of the universe to know?

How can we truely say "without borders" unless we have been out there to see that there are no borders? And how do we know that the "border" is not just 1km ahead. The point we STOP looking for boundaries could be just before we find one.

2. If it is "expanding" then what is it expanding INTO?

Lets say void. Then what is at the edge of the void? Has anyone gone into the void (or SEEN into the void) to find out if there is a boundary?

3. If it is an enlarging sphere of bent space then it is NOT infinate but it IS expanding, right?

If we DID travel in the same direction we could find "NO BOUNDARY" if we returned to the spot we started. But that would mean that the universe is NOT infinate, although its size is actually expanding.

4. We can specificallly PINPOINT how far we can see into space. As we have an ABSOLUTE number how can it correlate to an infinate universe?

Just because I cannot see the ocean from the middle of the country doesn't mean its there. I could walk for ages (3000 km in fact across Australia) and not once find the "edge" of the continent. Do I then stop and say "There is no border"... or have I just given up to early?

[kedaman]

Well if there's something outside universe then there isn't, if there's a border of universe there isn't. Because it does not matter as you can never reach it, if you go near you will only expand it.

I think space is unlimited in all directions and that matter is expanding inside it

If it is "expanding" then what is it expanding INTO?

If it was expanding into something, it would be hyperspace.
If not, I think what kedaman said was right. It's the matter that's getting futher apart.