Quote:
Originally Posted by bkadoctaj
In other words... addition is illusion. Addition is the only way to suggest that 0 and infinity are inverses, because the space between 1 and itself (1 + 0 = 1, according to conventional mathematicians) cannot be calculated. Addition means you must add something, and you must change something. That's why it's a function. 0 is a concept, like infinity, for that which does not exist in form. It is a "value" that cannot be compared to 1. The ratio is infinite, and no amount of multiplication will ever make them equal; thus the ratio, in and of itself, is nonexistent.
Any function has two essential parts, by my logic above: itself and its inverse. 1 has an additive inverse, but none exist for values greater than 1. Why is this? Because if you have 2, its inverse is -1. If you have 3, its inverse is -2. If you have -1, its inverse is 2. So, you either keep the positive or the negative numbers, because by their naturally inverted nature, each is the other, drastically simplifying the number system. Simplify the whole system and remove negative numbers. Scale everything to one.
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The space between zero and one is one, the same as the difference between one and two, two and three, or any other two consecutive integers. The problem with describing anything as the inverse of infinity is that infinity is not a number -- ie, it does not belong to the set of real numbers, so you cannot write a mathematical equation that uses it. You can only use it in the context of a limit, such as defining the set of positive real numbers as (0,inf), but the equation 1 + inf = inf does not prove anything mathematically or logically.
That being said, when talking about sets of numbers, negative infinity is generally considered to be the inverse of infinity. One's additive inverse is negative one. Similarly, two's additive inverse is negative two. Only when you delete zero from the process does the math become convoluted, which proves little more than the fact that negative numbers rely on zero to make sense.
Without a zero and the concept of negative numbers, math as we know it falls apart. Suddenly the equation 6 - 8 = ? has no solution, or is considered equivalent to 8 - 6 = ?, depending on how the rules are structured. One can come up with increasingly convoluted ways to do math without these two important concepts, but every civilization that wanted to do more than count things with math eventually discovered the need.
Hope that helps.