Re: INFINITY
There are two special number that are not numbers as we know, the infinity and the zero. Both of them are the universe fro their own.
If You have studied a course of mathematics on university, You coud remeber about the questions like wkat is $0/0$ and $\inf / \inf$/. Both relations in general have the posibility to yield a result that coud cover entire range of numbers including the $0$ and $\inf$. The behavior of functions that tend to zero and infinity could be studied, so in a simple words. if You look at two simple functions, $y_1(x) = x$ and $y_2 (x) = x^2$, You could simply conclude that the function $y_1(x)$ is going towards the infinity slower than the $y_(2)$, just start calculating values for $x = 1, 2, 3,...$. So if You study the behavior of both functions You coud yield a result that $y_1 / y_2$ tends toward zero as x tends towards infinity, and the reciprocial of that tends towards positive infinity.
Yes the infinity has its sign! It could be positive and negative.
And now the part that is related to Your question. Since the things that I am writing about I have studied somwhere in 1991. and 1992. (this part of mathematics I have studied on seccond Year of my studies [Physics]) I could Sugest You to try to find some more in depth literature on number theory and mathematical analisys.
The question about what is the infinity and how to characterise one type of infinity compared to other has bothered people for quite a long time. lets look at the simplest infinity that is known to men, set of natural numbers $'N = 1, 2, 3, ...$. It is infinite, but the infinity is not so complicated. Simply speaking You could try to enumerate (I am not sure that this is exact term, since I am not of English origin, I am from Serbia, so I am native Serbian, Slavic langage literate) every element of thet infinite set, and succeed in a infinite time. So it is the simplest kind of infinity. Yhen it is decided to mark this infinity with one Hebrew letter, the aleph with the index 0, I think it is written in Amsmath paskage (LaTeX) as $\aleph _0$. And a comparison with it started. Now goes the part that I am not so sure that I coukd interpret correctly...
Let's look at the set of rational numbers. Every rational number could be represented as a fraction of two natural numbers, and a sign, r = (+ / -) m/n, where both m and n are from the set of natural numbers with zero included (0, 1, 2, 3, ...). So You could conclude that the set of rational numbers that You are looking at could have an $\aleph _0$ values for every fixed value of n (or m if You like, it makes no diference which number that You took as a fixed one). And so with a leatle math theory You could conclude that the rational numbers are "more dense" infinite nubers than the set of natural numbers. To be more exact, since it is the $\aleph _0$ set divided by $\aleph _0$ set the density is square of $\aleph _0$ ($\aleph _0 ^2$). One remark, the entire natural number set (0, +/- 1, +/- 2, ...) has a densiti of two $\aleph _0$ but since $\aleph _0$ represents infinity any finite number added or multiplied or divided or subtracted from it does not affect it, so $2 \aleph _0 = \aleph _0$.
Now one step beyond. If You coud remember, the real number set is more dense than the natural and rational one. Inbetween anny two rational numbers, lets say r amd m You could have an infinite number of real numbers. Just look at the square root of any prime number, e.g. the square root of 2 $\sqrt{2}$ cannot be represented accurately with any rational number. How, You could ask. If I press an sqrt knob on a calculator I get a result. To be mathematicaly correct it is an rational representation of a real number with an error of a estimate. If You press the sqrt number for two on a calculator with a one significant number You will get a value 1.4 but with an error of 0.05 (sqrt(2) = 1.4 +/- 0.05). On a calculator with two significant digits You will get 1.41 +/- 0.005 and so on. With every finite number of digits You cannot get an exact value of sqrt(2). So it is like on every point of a rational number scale the real numbers growth an new infinity (the density of this "growth" infinity, if I could remember correctly is also $\aleph _0$). So in this case You have an $\aleph _0$ set on power of $\aleph _0$. If I remember correctly it is called an $\aleph _1$ set ($\aleph _1 = \aleph _0 ^{\aleph _0}$) but this part You coud check.
Simply speaking inside the infinity You have an infinite numbers of more complex overlaping infinities.
Also the zero is infinite number also. just divide some finite number with zero and You could get an infinite number.
Those two numbers are related. Everuthing sed for infinity could be applied to a zero. You just think of zero as infinity colapsed into a infinitely small point.
Simple?
I apritiate Your interest in such philosophical questions, and If You have an interest I encourage You to have a leatle in depth look on that matter.
Sincerely Yours,
Nenad Sakan