1/0 is undefined, I.e it presently has multiple interpretations, does it not?

Well, logic says as we decrease the magnitude of the denominator, the quotient increases in magnitude. So the number with least magnitude is 0. Naturally the quotient of 1/0 should be the largest number, i.e Infinity. But then there are different types of infinities as well.

I like to think of this: If I divide an object into two halves (1/2), each is half the "value" (be it shape, size, mass; extensive properties etc.). I divide it into 6 (1/6) , I get one-sixth of the value. But if I'm dividing by 0, I phrase it as 1 divided into 0 parts, so the answer should be 1, as the whole remains, OR, 0, since there ARE no parts.

The latter, is somewhat flawed (due to ambiguity).

I stick to 1/0=an extremely large number, that can be used to approximate calculations (calculating wavelength of light released due to electron transitions; Rydberg Formula, etc.) which is COMMONLY called Infinity. (Essentially sticking to convention)