Actual Infinity in Reality?

[GrandizerII]

Also, let me address this one as well:

For Zeno's paradox,  it was offered that calculus is the answer, and that a infinite small amount of time, and an infinitely small distance can be covered.  I don't buy it.   It doesn't matter if you have a lot of time, or infinitely small amounts of time, or however much time.  If you follow that procedure of infinitely dividing in half the remainder, you will never reach the destination.  It's not a matter of time.   This may also be demonstrating the issue above of using infinity as a number.  Also, you cannot have an infinite number of small distances in a finite distance, nor an infinite amount of time, in a finite time.  This is a contradiction.  Zeno in his paradox, was arguing that there was no motion.  And we can easily observe that his conclusion is false.  Not only can I set out to and reach a distance of 10 ft.  I may very well pass it.  Who are you going to believe "Zeno... or you lying eyes?"  There is nothing wrong with Zeno's math, the simplest answer is that there is a problem with his underlying assumptions.

Note that Zeno's paradox isn't an argument against a finite distance having an infinite number of smaller distances, or a finite time having an infinite number of smaller time instants. The argument is supposed to be against the possibility of traversing such a distance or time. And for that traversing bit, I leave it up to others to address for you.