Why, how do you do?

[fr0d0]

Oh boy. Please tell me the dissenters were kicked out.

Erm..

[BioLogos]

Is infinity really a number or simply a concept dreamed up by mathematicians that has no place in the real world?

Infinity is not a "number", but the concept of unboundedness. A set, S, is infinite if and only if |S|>n for any positive integer, n (|S| means the number of members of S) (i.e. the number of members of S is unbounded). Equivalently, infinity is the opposite of finiteness (S is infinite if and only if there does not exist a positive integer, n, such that |S|<n.

Infinity is also an impossible concept to get your head round, which is probably why it's represented by the love knot.

[Tiberius]

Since [0,1] is uncountable, there exist uncountably many points along any finite length in the universe. Why is this not a counterexample to your statement in bold?

Because there is no evidence to suggest that space can be divided into an infinite amount of sections. At some point, you reach atomic lengths, then the length of electrons, then...etc. Essentially there has to be some standard "smallest" length, rather than an infinitely small one, because otherwise physics breaks down and you get paradoxes.

Zeno came up with a few of them, namely Achilles and the Tortoise (dealing with space):

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox.

and the arrow paradox (dealing with time):

Zeno states that for motion to be occurring, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one instant of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. However, it cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible.

[BioLogos]

Because there is no evidence to suggest that space can be divided into an infinite amount of sections. At some point, you reach atomic lengths, then the length of electrons, then...etc. Essentially there has to be some standard "smallest" length, rather than an infinitely small one, because otherwise physics breaks down and you get paradoxes.

Is there any evidence to suggest that it can't? (Personally I don't have the foggiest about this issue, having only dabbled in a bit of QM. Does uncertainty affect whether we can determine whether spacetime is discrete or not? I have no idea. Is discrete spacetime accepted theory nowadays?) The paradoxes just challenge our intuition rather than form any kind of contradiction.

[Tiberius]

Is there any evidence to suggest that it can't?

Yes, namely that the paradoxes do not hold in the physical reality.

The paradoxes just challenge our intuition rather than form any kind of contradiction.

Erm...how about the contradiction that when you fire an arrow, it travels through the air, rather than not having any motion at all. If the arrow paradox held in the physical reality, movement would be impossible. Since this is not the case, it is not true that space or time can be divided into an infinite number of sections.

[Amphora]

Welcome BioLogos to the forums.

@Adrian for the love of GOD, no more with the 0.9999...... = 1, I beseech thy please stop!!

[Tiberius]

Ok, I'll stop.

By the way, did you know that 1.999... = 2?

[Purple Rabbit]

Ok, I'll stop.

By the way, did you know that 1.999... = 2?

Not in your lifetime.

[Tiberius]

But it does!

[Purple Rabbit]

Then write it out in your lifetime. Wait I,ll help you underway:

1.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

Now you finish it...in your lifetime!