(in the extended complex plane z/0=ComplexInfinity only by convention)

And we can actually count infinity! The set of integers Z and the set of quotients Q have the same cardinality (i.e. size) that is denoted by the transfinite number aleph-null. The set of real numbers R have a higher cardinality aleph-one. The set of real numbers in (0,1) have the same cardinality as the whole real number line!

Technically, we can label 1/0 as “undefined” and ignore the problem, but that may be similar to saying “3-5″ is undefined (prior to negatives) since subtraction is the inverse of multiplication.

That’s not quite the idea, though. 3-5 is well defined because there was an “obvious” convention once you look for consistent properties (3-5+5=3). There are times when 3-5 is still undefined (If you have three apples and you eat 5, then you’d better see a doctor… there’s no way to “owe” apples in this context), but if you look at it in a very abstract sense it always makes sense to have negatives there when you want them.

1/0 is not so simple. It’s well defined, but in a number of different contexts, none of which being the “obvious” choice. Any time a mathematician, scientist, or engineer ends up running up against a division by zero, they should know the context well enough to make the right choice for how to get over the hump. They may even decide it’s not worth it.

The point is that 1/0 isn’t all that crazy, it just takes more information than you get in the plug’n'chug mindset taught in high schools and their ilk. Nullity is nothing more than a default answer to a question that wasn’t properly asked.

Yes, the great irony is that traditional education can often kill the desire to learn, if taught in the wrong manner. I’m glad you’ve overcome that, and I’ll be writing more math in the future. Thanks again.