[lyner]

It's this keyboard, you see.    :-)

[justaskin]

There is not a coherent 'English' description of Infinity -

boundless,limitless.never ending,going on for ever, beyond imagination.

You have to go to Maths for a safe way to define it 

And that definition is?.
[quote
My two series of numbers each increase as you go further.
[/quote]
Yes

One increases faster than the other

Yes

so, however far you go, it is always bigger.

Yes and this defines infinity how?.

There are times, however, when you can use infinity more safely. For instance, if you add up the series of numbers

1+1/2+1/4 + 1/8 +++ you will never get a total more than 2 - even for an infinite number of terms. We can use the word 'infinite' safely because the final result is finite. That is a 'convergent' series, as opposed to a 'divergent' series like the first two examples.

Are you not just using infinity here to describe how large the series could be.could you not use some of the other descriptions such as limitless or boundless.Infinity has no roll in the actual calculation other than to describe its boundary yes?

Studying what happens 'on the way' to infinity can give you a clue about what would happen if you just carried on and on. . . .

And hence there is no need to and you can pack up and go down the pub for a beer. []

It's just too hard for a simple definition and you can't expect one any more than you can put Relativity or Quantum Mechanics in simple terms.

I think I have heard this used before to make people think they are inferior.
So what is the mathematical value of infinity?.
We have a value for Hubble's constant.
We have a value for the speed of light.
So what is the value for infinity.

Cheers
justaskin

[LeeE]

Infinity only makes sense to me as a dynamic value, which doesn't work as a static term.

[Soul Surfer]

With a bit of simple thought it is quite obvious that infinity cannot be treated just like any number in an equation

For example infinity plus one is clearly also infinity as is infinity plus any number up to infinity.  So it is clearly not possible to treat it in equations as the originator of this topic suggest so any conclusions are likely to be fallacious or at best partial.

As to the different orders of infinities these follow from the equations that control them as a mathematicion I can show how if I have an equation that "blows up" and becomes infinite at some value.  for example  1/x as x tends to zero I can easily create an equation that blows up faster by multiplying it by another number that blows up    say (1/x)^(1/x) as x tends to zero.

I can always increase this by rasing it to a power of 1/x  and so on without limit.

The answer when x=zero is always infinity but each of the infinite series of equations is always infinitely bigger bigger than the previous one.

This may be obscure mathematics but there are physical situations where this kind of thing happens.

[lyner]

I think I have heard this used before to make people think they are inferior.

No. To make everyone realise that they ARE inferior.
The only way to rise above this state is to realise our limitations and make the best of it.
There is no 'value' for infinity. How could there be if it is the result of a process which has no limit?

[justaskin]

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. []

Cheers
justaskin

[science_guy]

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 []) 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?

[syhprum]

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 !

[syhprum]

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.

[science_guy]

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]

Mathematically, chaps, I think we are all out of our depth.

[lightarrow]

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.

[science_guy]

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*

[JP]

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

[syhprum]

Thank you for clearing up that point it has perplexed me on and off for 70 years.

[alansm]

What is infinity? …  Half infinity doubled.
Is infinity plus one even greater?
Is half infinity smaller than infinity?
Is infinity just a concept?

[yor_on]

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:)

[alansm]

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!

[yor_on]

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.

[lightarrow]

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!  []