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Author Topic: What is infinity?  (Read 11498 times)

Offline justaskin

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What is infinity?
« Reply #25 on: 11/01/2009 01:31:40 »

There is no 'value' for infinity. How could there be if it is the result of a process which has no limit?
Hey I agree with that.Does that make me a mathematician. ;D

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Offline science_guy

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What is infinity?
« Reply #26 on: 11/01/2009 02:40:44 »
a concept of infinity that I always thought of on this subject (ever since questioning the math teacher, and him being unable to tell me much of infinite geometric sequences ;D) was that Infinite is any number than cannot really have an end value pasted on it... something like a destination, rather than a number.  just like the horizon, you know it's there, but you will never reach it.

say, perhaps, you have point a, and point b.  point a is 25 centimeters from point b. but it can also be measured in inches, half inches, millimeters, feet, tens of feet, in infinite number of ways, because the list never ends.

but then you have the size of infinity.

the 1+2+3+4 example is one way, but I thought of another definite way to put it. 1/0 is infinite, because of the process used in division.  in division, you essentially subtract the denominator from the numerator, increase the end result by 1, and then repeat until you cannot subtract anymore.

for 8/2, it would go like this:

8-2 = 6, result = 1
6-2 = 4, result = 2
4-2 = 2, result = 3
2-2 = 0, result = 4. can no longer subtract, therefore 8/2 = 4.

but for 1/0, it would go like this:

1-0 = 1, end result = 1
1-0 = 1, end result = 2
1-0 = 1, end result = 3
...

that cycle will never end, so therefore, the end result is infinite.

but say you turn it into 2/0, it would be a infinite that is larger, since, if you could put it another way, and you divide them, (2/0)/(1/0), then you divide the denominators, assign that as a value of 1, because any identical values divided will equal one, then the numerator becomes 2.  Therefore, theoretically, 2/0 as an infinity is twice as large as 1/0.

however, you can also say that 0/0 is an infinite, invalidating the previous paragraph.

but given the fact that I don't really yet know calculus, and haven't worked with infinity much, I don't know if my thoughts are really valid.

anybody care to correct me?
 

Offline syhprum

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What is infinity?
« Reply #27 on: 11/01/2009 07:29:59 »
As a school boy I tried to argue that zero times infinity was one from the arithmetical statement 1/0 equals infinity and 0/1 equals zero therefor 1/0 * 0/1 the zeros cancel out and one is left with 1/1 which equals one.
My argument fell on deaf ears !
 

Offline syhprum

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What is infinity?
« Reply #28 on: 11/01/2009 16:40:23 »
it is fascinating that a convergent series taken to an infinite number of steps (Zeno's paradox ?)can have a finite value ones first impression would be that an infinite number of steps how ever small would add up to infinity.
 

Offline science_guy

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What is infinity?
« Reply #29 on: 12/01/2009 16:02:27 »
I had also thought that, but what if you took differing "values" of 0 and infinity? the only requirement for that kind of argument is that for the 0, you must have 0 in the numerator, and for infinity, must have 0 in the denominator.  All of this, however, is more theoretical... I would think a lot of this is may be preconceived notions.
 

lyner

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What is infinity?
« Reply #30 on: 12/01/2009 21:17:21 »
Mathematically, chaps, I think we are all out of our depth.
 

Offline lightarrow

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What is infinity?
« Reply #31 on: 12/01/2009 23:33:55 »
As a school boy I tried to argue that zero times infinity was one from the arithmetical statement 1/0 equals infinity and 0/1 equals zero therefor 1/0 * 0/1 the zeros cancel out and one is left with 1/1 which equals one.
My argument fell on deaf ears !
300,000/0 is also infinity, so 300,000/0 * 0/1 should be equal to 1?
0* is undefined.
 

Offline science_guy

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What is infinity?
« Reply #32 on: 13/01/2009 15:57:29 »
yet there is another absolute of mathematics that that breaks. 0 times anything should be 0, so why wouldn't 0 times infinity be 0?

*calling all mathematicians*
 

Offline JP

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What is infinity?
« Reply #33 on: 13/01/2009 17:17:19 »
Infinity isn't a number in the usual sense of talking about numbers.  Multiplication is defined as something you can do when you have two numbers.  Therefore you can't multiply something by infinity.  What's very useful in dealing with the usual real numbers is that when you add, subtract, multiply or divide (except by zero) two real numbers, you end up with a real number as a result.  This means you can do any number of operations and be assured that you end up with a real number.  (In mathematical lingo, the real numbers are a field under these operations). 

What you're trying to do is to include ∞ as a real number so that you can do things like multiply by it.  You can do this, but then addition, subtraction, multiplication and division (except by 0) have a lot of exceptions that aren't defined as real numbers anymore. Here's Wikipedia's list of what is usually defined and undefined: http://en.wikipedia.org/wiki/Real_projective_line#Arithmetic_operations_which_are_defined
 

Offline syhprum

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What is infinity?
« Reply #34 on: 13/01/2009 17:32:06 »
Thank you for clearing up that point it has perplexed me on and off for 70 years.
 

Offline alansm

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What is infinity?
« Reply #35 on: 13/01/2009 19:17:09 »
What is infinity? …  Half infinity doubled.
Is infinity plus one even greater?
Is half infinity smaller than infinity?
Is infinity just a concept?
 

Offline yor_on

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What is infinity?
« Reply #36 on: 13/01/2009 21:26:44 »
Infinity is a very strange subject.
Yet it seems to me that we are surrounded by it.
Infinity, isn't that when we lose count?

So, the possible amount of stars, molecules, atoms, quarks.
We're looking up through the eye of infinity doing our best to count our way out:)
 

Offline alansm

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What is infinity?
« Reply #37 on: 16/01/2009 09:32:39 »
So, the possible amount of stars, molecules, atoms, quarks.
We're looking up through the eye of infinity doing our best to count our way out:)

If something is quantifiable, no matter how large a number, then it falls far short of being infinite.
Current thinking tends to speculate that even the universe is finite. Therefore the numbers of stars, molecules, atoms and quarks are also finite, as are the grains of sand in an hour glass.
If however, it turns out that the universe is unbounded and infinite then everything within it will also be infinite along with every permutation and possibility. This would also make the appearance of ‘life’ an inevitable certainty as every possible outcome would exist, regardless of how improbable. (Another topic?)
Infinity is more than very large - infinitly more!
 

Offline yor_on

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What is infinity?
« Reply #38 on: 16/01/2009 10:27:04 »
True:)
But who will count it down if finite.
An approximation will have to do.
But that's not the number.

So what we reach for, even if finite, will never be counted.
 

Offline lightarrow

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What is infinity?
« Reply #39 on: 16/01/2009 18:07:58 »
True:)
But who will count it down if finite.
An approximation will have to do.
But that's not the number.

So what we reach for, even if finite, will never be counted.
Why? If something is finite, I call it "n" and that's all!  :)
 

Offline lightarrow

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What is infinity?
« Reply #40 on: 16/01/2009 18:09:46 »
yet there is another absolute of mathematics that that breaks. 0 times anything should be 0, so why wouldn't 0 times infinity be 0?

*calling all mathematicians*
Because what you say is true only if "something" = number.
 

Offline Don_1

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What is infinity?
« Reply #41 on: 16/01/2009 18:16:02 »
Ah! Infinity, I could go on about it forever....

There is no 'value' for infinity.

Quite so, if you try to put a value to infinity, you are giving it borders, you make it finite, don't you?

Infinity cannot be explained by figures and cannot be conceived by man.
 

Offline yor_on

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What is infinity?
« Reply #42 on: 16/01/2009 19:29:43 »
Well, it has been conceived by man:)
Or at least, found out::))
 

lyner

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What is infinity?
« Reply #43 on: 16/01/2009 21:29:37 »
This may sound like a put-down but there is no way you can get a handle on 'infinity' if you aren't prepared to go through all the formal steps of Mathematical Analysis. It's hard and it's rigorous and it doesn't involve a single poetic superlative. Whatever fancy words you use to describe infinity, there is no way to relate it to the infinity of Mathematicians. I'm afraid that many of the contributors to this particular thread are way out of their depth. I include myself in that. Don't expect to get anywhere unless you are prepared to take advice and go through it from scratch.
 

Offline yor_on

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What is infinity?
« Reply #44 on: 17/01/2009 11:03:07 »
SC, you can't mean that?
'and in wells of her eyes, infinity unfulfilled'
I once saw a little book. 'Mathematics for poets (and dreamers)' (?)
A very nice one, I almost understood it.
:)
 

lyner

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What is infinity?
« Reply #45 on: 17/01/2009 16:34:44 »
I wouldn't trust the Author to predict the outcome of a bit of Engineering if that was their only claim to fame.

As with many words, "infinity" has two separate meanings. They apply differently to different cases.

You can't make a mobile phone work with poetry, can you?
We need both left and right brain activity.
 

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What is infinity?
« Reply #45 on: 17/01/2009 16:34:44 »

 

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