Randomness cannot be defined

"Borel's conclusion is that there can be no one definitive definition of randomness. You can't define an all-inclusive notion of randomness. Randomness is a slippery concept, there's something paradoxical about it, it's hard to grasp. It's all a matter of deciding how much we want to demand. You have to decide on a cut-off, you have to say «enough,» let's take that to be random."

Gregory Chaitin, Meta Math!, Complexity, randomness and incompleteness.