Division by Zero

What do you make of this?

http://file.okmr.yamatoblog.net/bso180102.pdf

The division by zero is uniquely and reasonably determined as 1/0=0/0=z/0=0 in the natural extensions of fractions. We have to change our basic ideas for our space and world.

I don't know what is the implication of division by zero as defined in that manner. I have never thought about it this way. I have always taken the definition that anything divided by zero is "mathematically undefined".