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Do You Have a Problem with Infinity?
- Thread starter Thief
- Start date
ratiocinator
Lightly seared on the reality grill.
What do you mean by deal with them? There are exactly the same number of even integers as integers in total. There are more real numbers from 0.0 to 1.0 than there are integers. The number 0.99999...[forever] is exactly equal to 1.
Infinity leads to odd results but it can be dealt with mathematically.
Thief
Rogue Theologian
there is some speculation of particles having be.......harmed
but the mass is not reduced
I'm not sure I buy that
Especially as revealed to us by set theory, which is apparently the basis of all mathematics, I think infinity, namely under the aegis of infinite sets, is a wonderful, paradoxical, mind-bending and unavoidable idea. The infinite is real, here and now.
Thief
Rogue Theologian
if you start with ......an infinitely small number....
a fraction of one
move toward....one
and you will never get there
Audie
Veteran Member
There's a lot of routes that will never get you to step one.
As a mathematician, I work with infinity all the time. There are consistent rules for infinite sets, but they are not the same as the rules for finite sets (why would they be?).
In the Banach-tarski paradox, a sphere is divided into a *finite* number of pieces and those pieces are rearranged into a larger (or smaller) sphere. The two spheres have the same number of points (an uncountable infinity, in fact), but the surprise is that only finitely many pieces are required and the pieces are rearranged by rigid motions.
In reality, the pieces would be impossible to actually make: they require infinite precision in selection of the points and there is no reason to think precision beyond the Planck length is possible.
Another aspect of this result is that it depends on the Axiom of Choice. In particular, an infinite number of fairly arbitrary choices must be made in forming the pieces. In essence, the pieces don't have a well-defined value for their volume (which is possible if the AC is assumed) and so the rearrangement is not limited by volume considerations.
In the Banach-tarski paradox, a sphere is divided into a *finite* number of pieces and those pieces are rearranged into a larger (or smaller) sphere. The two spheres have the same number of points (an uncountable infinity, in fact), but the surprise is that only finitely many pieces are required and the pieces are rearranged by rigid motions.
In reality, the pieces would be impossible to actually make: they require infinite precision in selection of the points and there is no reason to think precision beyond the Planck length is possible.
Another aspect of this result is that it depends on the Axiom of Choice. In particular, an infinite number of fairly arbitrary choices must be made in forming the pieces. In essence, the pieces don't have a well-defined value for their volume (which is possible if the AC is assumed) and so the rearrangement is not limited by volume considerations.
There are no infinitely small numbers. The set of real numbers obeys the Archimedian property.
Twilight Hue
Twilight, not bright nor dark, good nor bad.
The amazing thing is that you can have a finite set while at the same time you can have an infinite set. Basically you can count infinity and structure it with finite points. However it will always remain Infinity.
No, I have no problem with infinity. I don't work with infinite sets, or much at all with advanced mathematics, so I rarely run into infinities...I find that when I run into an infinity (say, for example, the value of Pi), pragmatically chopping it off at three or four places to the right of the decimal provides a very useful answer.
My awe and inability to really comprehend infinity of any sort has nothing to do with much of anything in my life...paradoxes may be a good way to stretch one's mind, but my lack of comprehension doesn't have a practical application, as far as I am concerned.
others' mileage will vary, of course...
Infinity works so well.
It would be hard to do even basic math without it, eg, differential calculus.
It would be hard to do even basic math without it, eg, differential calculus.
ecco
Veteran Member
RE:
Do You Have a Problem with Infinity?
The only people who have a problem with infinity are those who believe that after they die they will spend eternity (an infinite number of years) in heaven. They really do not comprehend that after a very small percentage of infinity, there will be absolutely nothing for them to do that they haven't already done repeatedly for billions of times.
They do not realize that they will become completely insane.
Do You Have a Problem with Infinity?
The only people who have a problem with infinity are those who believe that after they die they will spend eternity (an infinite number of years) in heaven. They really do not comprehend that after a very small percentage of infinity, there will be absolutely nothing for them to do that they haven't already done repeatedly for billions of times.
They do not realize that they will become completely insane.
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Thief
Rogue Theologian
GoodbyeDave
Well-Known Member
I don't have a problem with infinity: I just disbelieve in it. There have been enough mathematicians who have agreed with me to leave me feeling comfortable about that!