Actual Infinity in Reality?

[polymath257]

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1. yes, between any two real numbers, there are infinitely many real numbers. I agree.

2. Let's be more precise. Yes, whenever you are *between* 0 and 1, say 0<x<1, there is another point y with x<y<1.

3. Let's be more precise. Whenever 0<x<1, there is a point y with 0<y<x.

4. I agree with both of those as I stated them.

OK, so where is the problem?

So as we progress from say 0 to 1, there is always another point Y between X and 1 where X<Y<1.  
1. If you must pass through each of these points, you will never reach 1, because there is always another point Y which must be met.

Therefore Zeno concluded that if you can never end your journey or on the inverse (which isn't quite as intuitive) never begin your journey,
then motion is impossible.  If you have to complete a endless number of points before you can get to the end (1) then you will never be at the end (1)

Do you agree?   If not, where do you think that the error is?

Please be more precise: exactly what process do we use to go from 0 to 1? Be specific.

But yes, at any point there is another point to go through. And yes, we manage to go through all of them.

The problem is that you are assuming we cannot compete an infinite process. Look at my comments on the definition of 'infinity' above.