In my mind, zero divided by zero answers the question of what $a$, when multiplied with zero, equals zero:
$a * 0 = 0$
Obviously, any real number will satisfy this equation. However, one divided by zero is different. It answers this question:
$a * 0 = 1$
This is different, because there are no solutions. Both results are referred to as "undefined". To me, these two "types" of undefined are completely different. I realize that many applications don't care whether there's no results or infinite results. However, am I correct in my assumption that there are two types of undefined here? And if so, is there any terminology differentiating them that I can search for, possibly related to sets?
Question summary: Are there different types of undefined? If so, what are they?
I'm sorry if this is a duplicate. I've searched, but it's kind of hard when you don't know what you're searching for. I have read this question, but it doesn't mention any specific terms.