/sci/ - Science & Math

>>6616455
Should 0/0 be infinity?

For every n not equal to 0, n/n = 1. As n goes to 0, we see that 0/0 should be 1.

For every n not equal to 0, n^2/n = n. As n goes to 0, we see that 0/0 should be 0.

If x is any real or complex number, x*n/n = x. As n goes to 0, we see 0/0 = x.

So I think that clearly demonstrates 0/0 is quite problematic in itself. What about x/0? Well, x/0 = (x*n) / (0 * n) = (x*n) / 0. As n goes to zero, we see that x/0 = 0/0. So any definition of x/0 must be ill-defined since we have demonstrated it can be argued to be any complex number or infinity. Thus the reason it should return undefined is because it can't really be properly defined.