On Fri, 9 Mar 2012 20:42:53 +1100, "DavidW" <email@example.com> wrote:
>> So let me ask you some questions ... >> >> (1) Did the OP present anything that would qualify as >> a mathematical argument? > >Many times previously. But I'll pose a question: Is it >possible to have a container in which you can find all >natural numbers?
In theory, yes.
In the physical world, no.
But natural numbers are not elements of the physical world. They are conceptual entities, as are sets of such numbers. Mathematics allows for the conceptualization of objects such as the set of all natural numbers. It's the ability to create conceptual objects that gives math its amazing reach -- it's not tied down to physical realizability. The only requirement for a mathematical theory is that it not be provably inconsistent. In other words, if a theory yields no logical contradiction (within an accepted framework of logic), then it's legal.
As an example, consider Geometry.
In Geometry, a straight line goes on forever in both directions.
In the real world, there are no straight lines.
In Geometry, a point is an object with zero size.
In the real world, any object has positive volume.
In Geometry, we can have 2 points as close to each other as we please.
In the real world, distinct objects can get close but not arbitrarily close.
In Geometry, we regard a line as containing infinitely many points.
In the real world, a container with infinitely many objects is impossible.
Thus, the human mind has the ability to create conceptual objects which are not physically realizable, and then deduce logically consistent results about the properties of such objects.