Reply to Re: I gave up to the Computers National Olimpiad
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Another thing that can lead to confusion is the mathematical term for different sets. "natural" numbers, "rational" numbers "real" numbers. When DraconicDink said that negative numbers aren't irrational, he meant a different "irrational" than what algebra-people (algebraicians?) would consider "irrational" (and even more different from what a game theorist would consider "irrational"). DraconicDink's references to "real" numbers as "numbers which exist" is also different from what mathematicians consider "real" numbers. I don't think a number on itself exists. It's always part of a certain algebra, that is, part of a set, on which an operation is defined. Same thing with "natural" numbers. While it might sound like "natural" means "obvious" (which would be a 'natural' line of thought, if you get what I mean), the "natural" numbers aren't quite as obvious as they might seem.
Actually I mean exactly what mathematicians consider "real" numbers. In my maths paper my tutor said: "that complex numbers can also be called 'imaginary numbers' and that they are things like the square root of -4, which has no logical answer". He also said that a "real number" is a number which has a logical answer to it, for example, such as the square root of 4. I agree with you that numbers themselves do not exist. When i said "real numbers" I did not mean "real" literally. Numbers are simply a human concept that was invented to represent a X ammount of a certain unit (eg: ammount = 10, unit = dollars).
However, I agree with your point on natural numbers. For those of you that don't know (if there are any): natural numbers are whole numbers (1,2,3...), not "obvious" numbers. So 1.2, 2.5, 3.9... are not natural numbers.
Actually I mean exactly what mathematicians consider "real" numbers. In my maths paper my tutor said: "that complex numbers can also be called 'imaginary numbers' and that they are things like the square root of -4, which has no logical answer". He also said that a "real number" is a number which has a logical answer to it, for example, such as the square root of 4. I agree with you that numbers themselves do not exist. When i said "real numbers" I did not mean "real" literally. Numbers are simply a human concept that was invented to represent a X ammount of a certain unit (eg: ammount = 10, unit = dollars).
However, I agree with your point on natural numbers. For those of you that don't know (if there are any): natural numbers are whole numbers (1,2,3...), not "obvious" numbers. So 1.2, 2.5, 3.9... are not natural numbers.
