In my younger days, I used to argue that the universe could not possibly be infinite. I have changed my mind on this subject. I believe that the universe could certainly be (and probably is) infinite.
My old argument used to go something like this:
"Look at an atom, a baseball, a baseball stadium, a planet, a galaxy; all of these things have a finite length and width and depth. Any "thing" you can think of then must therefore have a finite length and width and depth. Even if it may be incredibly large, it is not infinite."
This may sound reasonable but it completely ignores the idea of what infinity is. Let's look at an infinite set of random numbers as an example. You can pull a set of 3 numbers from a random infinite set, for example, 371. 371 is a finite set of numbers but it is a part of an infinite set of numbers. Therefore it is possible, indeed necessary, for something that is infinite to be composed of finite parts. This is part of the simple beauty of infinity.
I believe that the universe can certainly be infinite and that which we can see, taste, and touch is only an individual part of an infinite whole.
*Stop reading here unless you want to experience mind = blown.*
I believe that it is possible to experience infinity but I am still working out how that happens. Obviously it involves experiencing infinity in individual parts as stated above. So, by this reasoning you can experience infinity but it will take an infinitely long time. Or will it? You can observe an infinite amount of points in a finite amount of time. You don't believe me? Look at a circle. Watch a tire on a car complete a rotation. That tire has an infinite set of points around it's circumference. But, if it has an infinite number of points that come in contact with the ground at some point during its rotation then how do ever observe the tire complete a rotation in a finite amount of time? Answer? I don't know. But we do. Anything you can think of could potentially be infinite. Draw a line on a piece of paper. Now divide that line in half. Now divide it in half again. Theoretically you could do this an infinite amount of times. Does this mean that you drew an infinite line? Nope, it's finite. Yet, infinity is contained within it. This leads me to a shocking, yet simple, conclusion. Everything contains infinity. Infinity contains everything.
Look at irrational numbers. The decimal places in irrational numbers are infinite sets of numbers. You could use a random number generator to generate finite sets of numbers. Now think about this; these random sets of numbers you have generated are already contained somewhere in pi or the square root of 2. You could generate infinite sets of finite numbers and this would still be true. Everything contains infinity. Infinity contains everything.
If you know a part, you can know the whole. The part contains the whole. The whole is made of the parts.
In this way I believe it is possible that reality is like a fractal.