The Infinite Meat Pie

This subject came up a some years ago among me and my friends. It was the concept of the infinite meat pie. The claim was that if an infinite meat pie existed, everything in the universe would be part of this meat pie. This could be true, but the concept of infiniteness doesn't require it, as we soon shall see.

First, I'd like to point out that since this is a thought experiment based on the pie already existing, I have no explanation on how this meat pie came into existence. Maybe it was created in the Big Bake, or maybe it has just always existed. Also this meat pie would have an infinite mass and that's another discussion altogether.

Lets get back to the claim of the infinite meat pie being everything. If this infinite meat pie has expanded continuously and infinitely in all directions it would indeed be everything. Imagine this though--a finite piece of the meat pie is removed. The pie would still be infinite in all directions, but there would be a finite hole in it somewhere where other things could exist. There could even be an infinite number of these holes as long as they leave pie between them and the pie will still remain infinite. There's also the possibility of having a meat pie that's only infinite in some directions. If you are near the crust of the pie you could be looking in a direction of endless meat pie but if you turn around the rest of the universe would spread out infinitely in the other direction. Since there is an infinite number of directions to choose from this also means that there could be an infinite number of infinite meat pies spreading out in different directions and there could still be a direction without meat pie.

By proof of contradiction we have determined that the claim doesn't hold.

The pie is a lie!