Actual Infinity in Reality?

[pocaracas]

Here we should introduce the concept of the infinitesimal. Let's call it dx. dx is simply the limit, as x goes to zero, of x, or, in notation: lim(x->0) x.

How would you describe the limit as X goes to zero?

I suspect that when you include this, we are not that far apart in our thinking about the topic.  That this allows you to end the infinite regression (or progression) and reach the destination.

The limit as x goes to zero only exists if two other limits exist: Limit as x goes to 0+ and limit as x goes to 0-; these refer to the side from which zero is approached.
If these two limits are the same, the function is said to be continuous. If they are not, there is a discontinuity.
If both limits are +∞ and/or -∞, then you have a vertical asymptote.

Much like the concept of infinity (∞), the infinitesimal dx is also just a conceptual aid, it's not a number.