Lama, quoting definition you downloaded from the web does not prove you understand them. I agree with ex-xian, prove him and us that you know basic math by accepting his challenge.
Kaiser.
Lama:So, what exactly is your point here?
We are drifting off mathematical grounds. My point is that mathematics is universal, it does not rely on individual intuition. Sometimes intuition helps us understand and discover mathematical constructs, and sometimes it prevents us from...
Lama, you are naive to think that mathematics is based on intuition. You can develop perferctly valid (and maybe applicable) mathematical constructs even with the absolute non-intuitive foundations as long as your constructs are consistent. There are even complete mathematical systems developed...
Lama:Mathematics is the interactions between the individual/universal, local/global, intuition/reasoning, induction/deduction, integral/differential, 0/1, Emptiness/Fullness, ...
Prove it! In mathematics, we have axioms, definitions and proofs.
Kaiser.
Lama, a computer has no intution, yet it is perfectly able to perform calculations based on mathematical reasoning and constructs. Moreover, every computer is guaranteed to have the same result for a given mathamtical calculation.
Kaiser.
Lama,
I will say it again, what you are doing is not mathematics as we know it - mathematics has nothing to do with intuitions, moreover, sometimes our intuitions prevent us from understanding mathematical facts.
Kaiser.
So you agree that your "mathematics" is not ours, since you are making out your own "agreement" as you go along. The problem is that no one seems to agree with you. This is exactly what you are doing wrong, you continue to use the same terms we use without proving that (the terms you are using)...