Model theorists would like that option, because it would mean we could talk about Rings using the language of model theory. However, in order to do that, we’d need to be able to say 0^(-1) is defined. The algebraists don’t like that because they prefer keeping the axioms “Everything times 0 is 0” and “Everything times its ^(-1) is 1”.
Man, I don’t know how you guys live without “sup” tags.
Another reason it’s undefined is:
15/3=5 is the inverse operation of 5×3=15.
So 1/0=X is the inverse of Xx0=1.
But everything times 0 is equal to 0, so there’s no possible value for X.
Man I love when math makes my head hurt.It totally seems like it should be dead simple, I’d have always just thought of the answer as 0.
Model theorists would like that option, because it would mean we could talk about Rings using the language of model theory. However, in order to do that, we’d need to be able to say 0^(-1) is defined. The algebraists don’t like that because they prefer keeping the axioms “Everything times 0 is 0” and “Everything times its ^(-1) is 1”.
Man, I don’t know how you guys live without “sup” tags.
Another reason it’s undefined is:
15/3=5 is the inverse operation of 5×3=15.
So 1/0=X is the inverse of Xx0=1.
But everything times 0 is equal to 0, so there’s no possible value for X.
I’m pretty sure every comment I try to leave that contains a link gets deleted as spam.