 # Does randomness need a domain?

Hello guys! I’m writing a master thesis about random generative design, and I have a few questions i hope you guys can help me with. Can a system generate a random number if it is not constrained by a domain. That is to say if its domain is (-∞,+∞)? When i say random, I don’t include pseudo-random generators.

Decageeks said; "Can a system generate a random number if it is not constrained by a domain"?.
IMO, this question presents an immediate paradox. A system is by definition not random.
A system is a group of interacting or interrelated entities that form a unified whole. A system is described by its spatial and temporal boundaries, surrounded and influenced by its environment, described by its structure and purpose and expressed in its functioning. Systems are the subjects of study of systems theory.
https://en.wikipedia.org/wiki/System

Moreover, there seem to be only a few truly irrational numbers. Pi is one of them, no repeats, an infinite domain.

But even Chaos theory allows for spontaneous “patterns” to emerge. Mathematics are funny that way.

This is actually a persuasive argument for a universal abstract domain of Mathematics and mathematical functions. Cause and effect produce a result, a new value by the combination of two old values. The more relative values, the greater the mathematical probability of acquiring measurable physical 'patterns"

Random does not define “possibility”. It defines “probability”. In the case of life on earth, the combinatory richness of the Earth’s inherent mathematical potentials, it was not just probable, but a mathematical “necessity” .

Hmmm, this has the potential of becoming an interesting discuss if Decageeks, returns to actually engage with what W4U shared up there.

This video came to mind as an example of the mathematical nature of reality and that randomness merely represents a mathematical probability factor.

A more detailed website. The plot thickens… 