1. Suppose there is an actually infinite body.

2. If we remove one finite part from the infinite body, the remainder after the removal of that finite part is either finite or infinite.

3. The remainder cannot be finite, since then the original body would have been finite and not infinite.

4. So the remainder must be infinite.

5. Now, if we reattach the finite part we removed to the infinite body, the infinite body either increases in size or remains the same size.

6. If it increases in size, then there are two infinite bodies, one smaller and one larger (i.e. from before and after we reattached the finite part).

7. But this means the smaller infinite has limits, which is absurd, since an infinite body has no limits.

8. So the infinite body must remain the same size before and after the finite part is reattached.

9. But this means there is a whole that is not greater than its parts, which is absurd.

10. So the original supposition is false, and an actually infinite body cannot exist.

Thoughts?