Absolute value bug?

[burtonlang]

I don't know if this is just my calculator, but check this out. It doesn't happen on TI-83/84s, and I haven't tried other 68k calculators (like the TI-92 or the Voyage 200), but I would assume they would behave the same.

When I try to find 1/0 , I get "undef" as a response, which would be the expected answer. But when I type 1/abs(0) , I get ∞. Now, I understand how 1/0 can equal infinity (1/∞=0 , so if x=1/0 , then x=1/(1/∞) , then x= ∞ , therefore 1/0= ∞), but how can 1/0 and 1/abs(0) return different answers? Is there some kind of bug with the abs() function? It returns abs(0) as 0 , so I don't see how this could happen.

[boozee]

I get the same answers as you. Maybe in some way higher math
that I could ever understand 1/abs(0) being infinity and 1/0 being
undefined have some application.

What do your other calculators show?

[Indra]

Actually there is no bug there. The answer is right.
Division by zero is not defined. When we write 1/0 what we mean is 1 divided by a number arbitrarily close to zero.

1/0.000000000000.....................0001
or
1/-0.000000000000.....................0001

so the answer could be +inf or -inf depending on aproaching zero from the right or the left of the Real line.

On the other side, 1/abs(0) specifies that we aproach zero from the right. So the answer is defined.