Infinity...

[toh6wy]

...Similar to how, considering 1/infinity can be assumed to be zero, as can (3 billion)/infinity, the probability of randomly picking a number from the set of all real numbers and arriving at 5 is 0%, despite being possible. And if you randomly pick a number fifteen billion times, it's still 0%! Arrgh!

Well, I can actually see how this works. The chance of picking 5 is 0% because it's impossible to pick a number *truly* at random from an infinite set. You just can't do it. And here's why:

It's like trying to roll an infinite-sided die, with one side for each real number. Now, you might have learned in geometry that the more sides a regular polygon has, the more it resembles a circle. So, you could say that a circle is in fact an infinite-sided regular polygon. So what would an infinite-sided regular polyhedron be? A sphere. So, this "infinite-sided die" would be a sphere. How could you possibly know what number a spherical die "lands on"? There's no way.

Phew! That's some serious food for thought.

 

[The Last Conformist]

Well, your certain to get a number. It's just that the chance for any particular number to come up is zero.

 

[MSTK]

Okay. I'll try this again. Because it is fun to type. Especially when you're in my kind of state. Which will remain illegal. So I will not describe my state. But I will describe my conception of infinity.

Imageine a line that is infinitely long. At every second, there is a 1/10^10000000000 chance (not infinity) that something will happen at a given inch of the line (say that it turns yellow). So if you are at the point of that infinte line, every second there is a 1/10^10000000000 chance that you will turn yellow.
So, it is very rare, right? Something like that happens extremely rarely, right? Wrong.
Theoretically, if a line is 4 inches long, and every inch has a 1/4 chance of being turned yellow every second, an inch in that line will most likely turn yellow every second. If a line is 8 inches long and there is 1/4 chance, two inches would most likely turn yellow every second.
So if you have a 10^10000000000-inch long line and every inch has a 1/10^10000000000 chance of turning yellow every second, then atleast one inch will turn yellow this second. But, as we should know by now, 10^10000000000 is nowhere close to infinity. So if you mutiply that long line by ten to get 1/10^100000000000 (I added a zero ), then there is the chance that 10 inches will turn yellow. But still, it is not infinity.
If we multiply that really long line by infinity, how many inches will turn yellow every second? An infinite amount of inches. In a line that is infinitely long, something that has a 1/10^10000000000 chance of occuring every second occurs an infinite times every second. No matter how rare it is (heck, it could be 1/infinity), it will happen an infinite amount of times every second. And you know what? The line will never turn completely yellow.

So now let's move from the linear method of infinity to the planar. We are squaring infinity, now. Pretend there is a peice of paper that is infinitely wide. How big is it? If every square inch had a 1/infinity chance every second of turning blue, for instance, every second will have an infinite amount of squares turning blue, and yet it will never fill up the entire paper.

Now let's cube it to apply it to the 3-dimensional world. The same concept, but now infinity is bigger.

 

[Ren]

Just think of it as an inexhaustable(sp?) source of value.

∞ + 1 = ∞
∞ - 53 = ∞
∞ ÷ 2221 = ∞²³
∞²³ [Infinity^23] = ∞

and so on.

But:

∞ - ∞ = 0
and
∞ ÷ ∞ = 1

 

[Duddha]

Evidence? Present cosmological models suggests it's infinite in both time and space.

No matter how you cut it, the Bing Bang model is of a finite universe. Evidence, mmm, background radiation.

 

[pboily]

∞ - ∞ = 0
and
∞ ÷ ∞ = 1

careful, ∞ - ∞ and ∞ ÷ ∞ are indeterminate forms, like 0 ÷ 0 or 0^0... they can't be assigned a value.