Quote:
Originally posted by Greg700
It is obvious, but in order to show that your system of math is able to accurately represent this truth, you have to be able to prove it using that system.
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I don't know. It seems like proving "one" would be similar to trying to prove "blue". It is defined by the definition we apply to it. If it is red, it is not blue. If it is two, it is not one. It is blue because it is blue. It is one because it is one. It is only one because it meets the conditions that we use to define one.
Incidentally, i once read a book called "The Mathematical Experience" and there was a brief chapter on "pure" mathematics, that is, mathematics with no possible application to anything. It seems there are elitest mathematicians who look down their noses at math that can be applied to science and the human condition. These mathematicians will study their little area for years, perhaps decades, carving out their little niche. Eventually they get to a level of understanding of their particular specialty that is equaled by only a handful of other people on this planet. Then they die and maybe a handful of people will ever be able to understand and appreciate what they did in their lifetime. Their life's work probably amounting to nothing more than a footnote in some math history book.