I tested this theory.
I went and cut my dad's car in half. To my horror, I did not have two cars, and so he was angry.
I then tried to cut a table in half. I didn't get two tables for my trouble.
I attempted to cut a sausage in half. Did I end up with two sausages? I wish.
I tried to cut a tree in half. Boy was I surprised when I found that there was only a single, and also dead, tree.
I cut the cat in half, and it died. I didn't get two cats.
I cut a pizza in half. Once again, I didn't end up with two pizzas, which is a damn shame because I was very hungry.
To satisfy my hunger I then went and cut a sandwich in half. I ended up with two sandwiches, which I then cut in half again, and again, until I had 1024 sandwiches to eat. World hunger was solved forever.
One of the above is simply impossible. To help you, I highlighted it in yellow.
One sandwich cut in half is still one sandwich.