Infinity minus infinity

In this note, I consider an argument advanced by William Lane Craig and James D. Sinclair against the possibility of actual infinite collections based on Hilbert's Hotel and alleged problems with inverse operations in transfinite arithmetic. I aim to show that this argument is misguided, since it is based on a mistaken view that the impossibility of defining âˆ0 - âˆ0 entails the impossibility of removing an infinite subcollection from an infinite collection.