Given that 0 x 0 = 0 and 1 x 1 = 1, it follows that there are numbers that are thier own squares. But then it follows in turn that there are numbers. In a single step of artless simplicity, we seem to have advanced from a piece of elementary arithmetic to a startling and highly controversial philosophical conclusion: that numbers exsist. You would have thought that it should have been more difficult. A.W.Moore reviewing Realistic Rationalism
Ah, jeez. Ok students, let's start class.
First lesson, what are numbers?
Numbers in and of themselves are a mere symbol for a method of measurement; something that in and of itself is intangible, but with the symbology of numbers is now made visually applicable and not mysticized by imagination or rationalized thinking. The same goes for letters and the like, so you need only think of something intangible, symbolize it by whatever methodology and vwalla! Instant visual perceptability. Do you see? Numbers only exist as symbols, but they exist because a person created not only a method by which to use them, but a symbol by which to mark them. How'm I doin' so far? Any questions?
Ok, Next lesson.
Some people may say or deny that these statements are false, but they have very little argument when it comes down to the final blows. Yes, humans created numbers and a method with which to use them, but the common denominators or common factors existed long before this was made possible, so what was created was to measure something that already pre-dated this human invention.
Thank you, you have been a great class. Post any question you have, and those that I am able to answer I will and those that I can't I will post that I am unable to answer that due to lack of understanding in that field.