One Divided By Zero
Dear  [Lynn],
The night out at the ball park was very nice. Didn’t follow the game much. But did hang out with the family and friends, and talked to a retired mathematician about the 1 / 0 issue. He says that in real number theory, 1 / 0 is neither 0, nor infinity. It is instead, to use his word, indeterminate. The answer is undefined. He went on to say that while the calculus notion of the limit of 1 / x as x approaches 0 is definitely infinity, x never actually hits zero, but only approaches it. The problem is that 0 is a very special number. As long as x only approaches it, x is always some magnitude. But when x actually becomes 0, now we’ve crossed a border line of sorts, between having SOMETHING in x, to having NOTHING. So, while talking of dividing SOMETHING into NOTHING, as in 0 / 1, makes sense, how do you quantitatively discuss what the result is of dividing NOTHING into SOMETHING as in 1 / 0? While any number other than 0 has SOME magnitude, even those numbers very close to zero as in 0.0000000000000000000000001, 0 itself is a NOTHING number and does not behave the same way in real number theory as all the other numbers do. Wow, this is heavy. But I like it. 
Talk to you later.
Â
Tom