You know how a stopwatch goes like crazy with its hundredth numbers. They zip on by a hundred numbers per second. This is like infinity; it just does not stay put. You think you can add a number to it, 1 or a billion--it doesn't matter, but infinity is already way down the road. It does not stay put so you can do anything with it. + infinity, or - infinity are forever down the number line. Same goes for limits as the famous sin(x)/x. x can approach zero by moving the decimal point over to the left at the rate of a billion zeros per second--forever. It just can never equal zero, and conceptually, it never will.
What do you think is normalization? How does Hawking explain it?