The term "infinity" isn't reality?

Question

I'm sure you've seen the example of:
1/3 = .3333333 to infinity, hense
1/3 + 1/3 + 1/3 = .99999999 to infinity
But, clearly, 1/3 + 1/3 + 1/3 = 1
Doesn't this simple example, along with other similar examples, actually demonstrate that when we speak of "infinite numbers" or "infinity," we are creeping into into the realm of philosophy and out of the realm of math and reality?

Answer 1

I agree with you. Infinity is just a concept, it cant actually be attained. But your example is misleading you... decimals cant accurately describe the idea of "one third", which is why if you multiply 0.333 (recurring) by three, it doesnt perfectly equal 1. But this is a problem with the counting system, nothing more. If you actually had an infinite amount of threes trailing that decimal point, and you multiplied that by three, it would equal 1.

I've confused myself...

If you spend hours thinking about infinity like I do, check out a question I asked a while ago... some of the answers are interesting... http://au.answers.yahoo.com/question/index;_ylt=Ag4derL98OXo3ijnhIrCt7bg5gt.?qid=20060607215844AARjfHE

Answer 2

Be careful: you are confusing the representation of a number with the number itself. For example, take the number 1

1=1/2+1/2
=1/2+1/4+1/4
=1/2+1/4+1/18+1/8
and so on...
=1/2+1/4+1/8+1/16+...

Just because you can generate an infinite representation for a number doesn't mean it's not a finite and well-defined value. Indeed, there are techniques for summing infinite series which show that .333...=1/3 exactly.

In fact there is a very good example of a practical mathematical infinity: any segment of a continuous curve contains a "non-countable" infinity of points (because you can always find one number between two others, no matter how close together they are--there are always more decimal places, right? So if you were to try to count "all the numbers" from 0 to 1, you'd never get a measurable distance from 0. On the other hand, the set of counting numbers is "countably" infinite--here we can get from 1 to 2 and move a definite distance along the line, but we'll still never get to the end.

These things can be proven in mathematics, so there is some "mathematical reality" to the infinity concept. Is there plain "reality" to it? Does it matter?

Answer 3

I think you missed an important point. .333333333333 to infinity does not mean the value of the decimal number is approaching infinity. It means only that there are an infinite number of threes after the decimal point. The value of the decimal point you gave is actually approaching, but never reaching, 1/3 with each additional 3.

When you add .3333333333333 to infinity three times you'd get .99999999999999 to infinity, or pretty close to one...at least to the point where you'd be unable to tell the .99999999 etc. from 1.00000000000 to infinity.

Even so, the concept of infinity does encroach on philosphy a bit, especially if one considers philosophy to be an assertion that cannot be proved. For example, is 2/0 > 1/0?

Not really, both terms result in infinity and, here's where the philosophy comes in, how can one infinity be greater than another infinity? But for 2/m > 1/m, where m is any real number, the inequality is true. If m = 2, for example, we have 2/2 > 1/2 or 1 > .5, which is clearly true. One is definitely bigger than point five. So why then, does this not hold true when m = 0?

Typically, when mathameticians and scientists find an infinity in their results, they call the answer indeterminable. There are ways to work around infinities in equations. They involve limits, but that is beyond the scope of this answer.

Answer 4

The term "Infinity" could be used in math or in astronomy.
So it depends on where you use it.

Perhaps the examples used are not the best ones, but there are certain mathematical entities with limits tend to infinity.
So in essence, you are asking if the term "infinity" is applicable to the universe?

That question pushes you out of math and into philosophy and reality.

Personally, I believe the universe is infinite and keep growing and at the same time infinitesimal is being generated with stretching space.

I could only resort to my "intuition" which says both infinity and infinitesimal are related to reality via geometry. It is amazing, but not so mysterious. Because, it seems they fit very well together -- much like "conservation of energy". Then again I could be totally wrong too...

Answer 5

We are certainly not creeping out of the realm of math. Infinity as a concept is just extremely useful in mathematics--calculus would not be possible without it. As for your example above, .9999999... = 1. This is not a contradiction, just two ways of representing the same number.

We can't say whether there are any infinities in reality as an infinite quantity would be beyond our ability to measure. One potential candidate for infinity is the size of the universe. Another is the time until the universe ends.

Answer 6

I would say that what is called the realms of philosophy, supernatural, religion ETC. Are simply those which we do not yet understand with logic and mathematic prediction, so it’s not a matter of moving from one realm to another, but rather moving from the understood of what is to the not understood of what is.

Just because it is not easily explained now dose not mean it belongs in some mystical universe of things that never will be explained.

As for your example: 1/3 is not the same as .33333 repeating. One third is a third of 1. 3 thirds of one make a whole. But our decimal system works in intervals of 10 so .33333333 is really 3/10, 3 dose not go evenly in to 10 and so you have to settle with being infinitely close (and infinitely far away), but just not there.

Answer 7

Very good observation, LeAnn. I have trouble with the concept of infinity as a mathematical construct, because infinity squared should still equal infinity. If the universe were infinite in extent, then there should be an infinite number of planets identical to Earth in every way, including an infinite number of me typing this answer right now. I suspect the universe is actually finite, in which case infinity is imaginary.

Answer 8

How can you be sure that the universe came about without any connection at all to all it has living in it? There wasn't us and then the universe was there? On the other hand it may have been successfully scientifically completed and deliberately to accommodate us? Some physicists refere to our univers as the 'Antropic Univers' ie from its initial Big Bang state it is all primed so that we can live in it the way we do and who we are. And do not forget the complexity of our bio/mechanical/chemical structure too who is its product and made from the dust of the stars; and all that houses the intangible intellect too. Even if it is too remote for us to follow all the connections clearly our intuition and our basic knowledge can imagine a way past the molecules of life to that intangible core we refer to as the soul where all our faculties meet. Scientifically,deliberately the universe and us included are consiouse of each other; in my view. Peace

Answer 9

By definition, .333... "to infinity" means the same as 3/9.
same for .444... "to infinity", and so on.
So .999... "to infinity" is the same as 9/9 which is 1.
Infinity is not a real number if that's what you mean, but it is a real mathematical concept and well as a philosophical concept.
Keep taking math classes and you'll see how important the concept of infinity is in mathematics.

Answer 10

No, this is definitely well within the bounds of mathematics.

However, infinity does not have a single meaning. It can be shown that some infinities are larger than others - this was work originally done by Cantor using set theory. HIs work is vital in understanding some advanced concepts in physics.