Paradoxes!

Well, if something just doesn't work even though everything is right, you've found a paradox.

PARADOXES-

If you have a fully booked hotel with infinite rooms and infinite people arrive to get a room, you can just move everybody (who was there beforehand) in their rooms 'n' into rooms '2n' and fit them in.

If a person says, "This statement is false," then are they lying?

If you have a perfect machine that for a half-minute is on, for a quarter minute is off, then an eighth minute is on, and et cetera, will the machine be on in two minutes exactly?

sum (n=1 through infinity) (-1)^n = ? but the equations below are the same with different answers.
(1-1+1-1...) is the same as (1+(-1+1)+(-1+1)...=1) is the same as ((1-1)+(1-1)+(1-1)....=0)

Adam owns a shop with two employees, Bob and Carl. There are two rules for the workers.
Rule 1: There must be a worker in the shop at all times.
Rule 2: If Adam is out, Bob must be out.
Let's say Carl is out. By logic, if Adam is out, then Bob must be in and out, so Carl can never leave the store. However, the fact that Carl is out leads to the fact that he can't be out.

Let's say a faraway galaxy has two 'rules of sand'.
Rule 1: One grain of sand is not a heap.
Rule 2: Adding a grain of sand to a pile that is not a heap does not make it a heap.
Let's say you have a grain of sand, and add infinity more to the grain, one by one. That would mean infinite grains of sand are not a heap, which means that there is no such thing to distinguish a heap from a pile, thereby saying that the laws that proved it are unnecessary.

There are oh so many, and some of them were so confusing I barely looked at them. In fact, I am still confused by the Shopkeeper's Dilemma (with mah gals Adduhm, Baubbe, and Caurel).

That's all for our second post as of hoy!

Stay coolio,
John