Exactly right, Ricky. What I would like to have said if I could have chosen the words.

If someone clearly states their assumptions/beliefs/axioms and then carries on from there to explain their new ideas, then there is no argument.

If, for example, you build up a theory that excludes zero, we are all keen to listen. But then someone may say "ah, but what happens when you subtract 1 from 1?", and you need to provide an answer that works within your new framework.

In fact, let us build up such a theory. In this theory I say that a number is the set {x,u} where x is a real number and u is an always unique infinitesimally small number. I could then say that it is impossible to subtract any two such numbers and achieve zero. But then you may discover some flaw in my theory that makes it impossible (which is likely). But if we discuss this back and forth we may end up creating a new and wonderful branch of mathematics! In fact ...

No, no!
Maths is not "invented" by a human.
It's somthing abstract, you can't feel it, touch it, but still "it's there"!
The signs and the equations are just one picture of the math, which the human created.
Mathematics is some kind of invariant. It's unchanged over the universe, it's abstract, and doesn't depend, for example of the length of plank (as in phisycs). It's a mental ocean of knowledges.

But I've ever asked some kind of weird questions : how far can math go? which are the boundaries of the abstraction? Can we do everything with it?
And the other question - what is the structure of mathematics? So far we're proving beautiful theorems in different fields of maths, but no one (with little exeptions) has fully understood a field - that is, to form some kind of intuition to answer some questions whitout proving them.
And another - what is the mathematics made from? And who controls it?
There are weird mathematical paradoxes too, which ;ie in the foundamentals. For example the Goedel's incompleteness theorem - that we can't have math that proves or disproves everything - that maths has limits.
Another interesting contemporary structures are so strange, that nothing can be proven about them at all.
I'll give you an exampe: the infinite random sequence.
Many paradoxes are connected with it. It's proven, that the mantissas of almost every real numbers are such random sequences. But in fact, such sequence is unconstructible! There's no example of truly random infinite sequence!
Another example, which is more fascinating, is the halting probability : the probability arbitary computer program to halt.
It is shown that this probability exist, and is between 0 and 1, but is algoritmically unpreictible - that is, we'll can never know what is, for example, its 100th digit!

Is the mathematics inconsistent? Nobody (with little exeptions) knows. And we can't be sure until we find a crack in it.
But after 30000 years evolution, we've still not understood the "mattery" of the mathematics - the language of the universe we live in.

Very nicely said, krassi.

Yes, random number generators are faced with problems such as repetition, predictability and so on. But I have a theory that is because if you can write it down it becomes static and true random is dynamic. Just a theory.

Ricky wrote:

Random number comic

I absolutely love xkcd!