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Originally Posted by virtualmeet
I don't agree with this for the simple reason that a "consistent systems" is a system that all it's rules have to fulfill our mathematical postulates and laws...so we can only say that thoses "systems" are "deduced" and not invented.
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The only inescapable basic thing in mathematics is logic and the principle of non-contradiction. Without defining and constructing anything, you have nothing beyond logic. Peano's axioms are the standard way of defining the natural numbers, that isn't a "discovery" it's an invention! The same goes for integers, rationals and ordinary arithmetic, next come the real numbers(by topological completion of the rationals). The only reason it doesn't seem that way is because the natural numbers and arithmetic are so very fundamentally useful in describing basic facts of reality. They were constructed that way because they are very useful, that way.
Like any language, German, Hindi etc... it can be used to represent facts about reality. A mathematician is however not in the least concerned with reality. The sentence "Every cow is an excellent Tango dancer" is a perfectly correct, spotless English sentence, regardless of reality.
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Inutil insegnŕ al mus, si piart timp, in plui si infastiděs la bestie.
Hypography Forum PITA...... er, Administrator.
