Aristotle is said to have been first to make a distinction between the two, and he denied existence of actual infinity.
- Actual infinity is that which exceeds and always has exceeded all finite measure. Or mathematically: a property p of object is actually infinite, if, for every natural number N, p exceeds N.
That to me implies absence of something that can be called end or start.
- Potential infinity is that which exceeds a measure on every iteration of measure. Or mathematically: a property p of object is potentially infinite, if, for every natural number N which exceeds p, there is a natural number M exceeding N, which also exceeds p.
One could also say that potential infinity, as the infinite presented over time, refers to a process, whereas actual infinity indicates completion of a process, infinite at a moment in time,.
<font color=blue>As far as current theories go the universe is "actually" (*g*) infinite.</font color=blue>
Well, that to me implies that it had no initial state, and consequently God could not have initiated it *scratches head*.
Also, under no circumstances could he have afforded himself the liberty of stretching it out over the time period of six days. Thus Bible sucks, violently /php-bin/shared/images/icons/uhoh.gif.
<font color=blue>Creation as you are using it here requires that something happens over a period of time.</font color=blue>
No, unless I have somehow screwed up with the definitions. It requires that universe had (*errm* and still has) initial state, caused by God.
<font color=blue>Just because it is this way with what we believe is the universe, doesn't mean it is the whole reality.</font color=blue>
In that case, again, the universe needs to be defined first, I think.
<font color=blue>Why does everything have to happen in our limited understanding of tghe space-time continuum?</font color=blue>
Because, any arguments to the contrary absent, anything that does not and would never manifest itself in the space-time continuum, could be referred to as not existing to us existing in said continuum.
<font color=blue>Why do things have to "happen" per se at all?</font color=blue>
I love answering rhetorical questions in annoying manner: so that they manifest themselves, in the universe.
<font color=blue>Stephen Hawking has written a facinating book in which he tries to explain some theories of his which go far beyond our understanding and even attempted (and in some cases succeeded) to mathematically prove that there is more than our 3D+Time system, or even less.</font color=blue>
I have not read the book, unfortunately. Correct me if I'm wrong, but the conclusion he made was that there would be no place left for God. So, if it is his theory that is used to support the existence of God, it would have to have been someone else who made that conclusion. It would not automatically make such a conclusion false, but it would be interesting to know who and how; if I'm to gather the will to start learning about Mr. Hawking's theory.
More to follow ...