If a piece of matter is infinitely divisible it has infinite parts in actuality — Gregory

A subtle distinction is being overlooked here, which is, what I take to be, the root of your mistake. What's divisible into, say, two parts, isn't actually divided into two parts, for it was, then it wouldn't be "divisible" into two parts but actually divided into two parts. This subtle distinction, between being "divisible" (which is a possibility, as in being capable of being divided but literally being divided) & being (actually, not potentially) divided, should lead one to see that what's potentially infinitely divisible isn't actually infinitely divided. Comprehending this is the key to understand that what's potentially infinitely divisible is never actually infinitely divided, & therefore it's never actually made up of infinitely divided or separated parts but only potentially; &, moreover, if one pursues the division of what's potentially infinitely divisible into discrete parts, they'd always be at an actual finite amount at any point in their progress.

Which reinforces what I wrote earlier in one of my replies to you...

Also, Aristotle's point was that a potential whole is only potentially composed of parts, & not actually — aRealidealist

Meaning, a potentially infinite whole is only potentially composed of infinite discrete parts, but it's never actually composed of so many parts.

I already refuted all you just said. It's like talking to a rock. If parts can be divided they are there

It's like talking to a rock. If parts can be divided they are there — Gregory

... says the wall who's incapable of grasping that what can be parted isn't parted. The only thing that you've refuted is any claim of yours to logical competence.

Does what can be parted exist before parting

Indeed, as a single, undivded thing.

Then all the parts are there unseparated. Now does an object have infinite unseparated parts

Now does an object have infinite unseparated parts — Gregory

If there are "unseparated parts," how would I know how many parts there are, infinite or otherwise? If they're not separted or divided, they're not parts; if they're separated or divided, they're parts. "Unseparated parts" is an oxymoron (another logical blunder); as all parts are separate from each other, despite how deceiving appearances may be.

The lengths are still there. How many parts a thing has should finite but Aristotle says its infinite but only potentially so. A part of say a bicycle doesn't exist potentially however; the whole bike exists and all its parts. If it can be divided infinitely it has infinite spatial parts

the whole bike exists and all its parts — Gregory

The whole bike exists, or rather all of its parts. Yet, again, the parts themselves can be divided, even if they actually aren't divided; & until they are, they're a single or undivded thing. & so there's an actually finite, but potentially infinite, amount of divided parts composing the bicycle.

A part of say a bicycle doesn't exist potentially however — Gregory

However, an extension in the distanced traveled or moved, such as either the revolution about the surface of Gabriel's horn or the rotation about its axis, can most definitely subsist, that is, can remain, as a potentiality; & therefore it may approach or tend to infinity but without ever actually being infinite. This is precisely what you're missing about the case of Gabriel's horn. The extension of its surface area is potentially infinite, as it can just keep going on & on, but it's never actually infinite.

If I cross from A to B there are infinite halves I have to cross. This is easy to prove. The mystery is that it is finite, not that there are infinite halves. The infinite halves divided have space between and have theie same size when together. And what is that size?