Infinity and the Number Line
People have long tried to define infinity. Most people have the false conception that it is the highest possible number. The following sentence is the true definition of infinity. Infinity is a specific way to define an expression that could not be defined otherwise. For example, why do mathematicians say that 1/0 is infinity when no number could possibly be substituted into the quotient? That is because infinity is not a value, but a way to make possible impossible things.
Infinity also equals negative infinity. The following is the proof. I will use the @ sign as a substitute for infinity.
Infinity can not be defined as 1/0. But it can be defined as x/0
0 * @= x
This meaning to say that 0 multiplied by infinity is all real numbers.
If negative infinity is equal to negative x over zero, then you get -@ * 0 = -x. Then you just have to multiply by negative one on both sides and use the associative property of multiplication to get -@ * 0 = x. So they are equal.
If infinity and negative infinity are equal, then the number line must be circular. Infinity and negative infinity are the same point and zero is on the opposite side. Now you have the real number "line."