Real Number Field Axioms

I discuss the real number axioms. This is a formal way of developing the real numbers--technically, if you perform any operation that violates these axioms, UR DOIN IT WRONG. Of course, these agree with our intuition about numbers, but axioms allow us more power over our thinking. It should also be noted (for this level) that these axioms are necessary but not sufficient to describe the Real Number system. These are what are known as "field" axioms, and there's more than one type of field. Real Numbers also require certain axioms regarding order and certain axioms regarding upper bounds of sets of real numbers. For instance, rational numbers also obey all the rules discussed in this video, but they are not the same as the real numbers.