"How to distinguish between the complete and the incomplete infinite binary tree?
"How can we distinguish between that infinite binary tree that contains only all finite initial segments of the infinite paths and the complete infinite binary tree that in addition also contains all infinite path."
But there is no difference between them anywhere outside of WMYTHEOLOGY.
If there were, one would also have to have a difference between the set which contains all finite initial segments of |N and |N itself but the only place such a difference is claimed is in WMYTHEOLOGY and the only one claiming it is WM.
So the moderators were quite right to dump the article.