You can create an operator that can be made of other operators cardinal of A intersection B == cardinal of (A) (or cardinal of B : since A~=~B implies card( A

You can create an operator that can be made of other operators cardinal of A intersection B == cardinal of (A) (or cardinal of B : since A~=~B implies card( A )= card( B) ) This is your test re-expressed by using math. But basically the formula I gave is the shortest non factorable form of this operator in a normal set theory. And there you have a problem, every truth are biased by a corpus of prejudice called theory and the physical nature : because of the nature of computer you cannot represent any given number. There always be a number that can saturate your computer resources. It is called MAXINT. Old MAXINT where the size of a register. With Big Int there are the size of your allocatable computer memory (phys + virt)..... on a distributed grid it will be the resulting union of resources. And universe being resource bound there always be a limit to the representation of the integer you can make. So computers will still fall short of resources to represent ALL numbers. So the absolute operator you call for does not and cannot exists as long as computer are resource bound. So there is a map problem here that cannot draw completly the territory. The playground of physic is bounded, math abstraction/measures are not. And your way of interpretating data can be wrong : what tells you the input number are not modulo something? Like in a % 2 universe : 2 == 0 [2]. Good software are high context software. There is no such thing as immutable truth and monads is still an elucubration of a monk that ended being burnt by the church for blasphemy. Not to say he was wrong on saying the earth is moving (in fact the solar system)... but to say ignoring context can literally burn you. PS Noise is defined by the observator. It is measuring the log of the ratio of non of relevant choices over relevant choices (entropy) and entropy varies according to what the observer calls relevance of the data. What is relevant to someone (random numbers in cryptography) maybe irrelevant to other ones.