I say neigh (sorry if you didn't catch that joke, I'm a little horse).
If x/0 =0 then, since division is inverse of multiplication x= 0*0 this fails to hold for any x not 0
But the story says there is no defined multiplicative inverse of zero (undefined) so that they are free to choose any value they want. And they choose 0.
This is unsatisfactory to me because it seems to break the intuitive pattern of x/n getting larger as n approaches zero from the positives. 1/4 .25< 1/3 .33 < 1/2 .5 < 1/1 1 >1/0 0 >1/-1 -1 < 1/-2 -.5 < 1/-3 -.333
You see that sign flip thingy happening around 1/0?
I say neigh (sorry if you didn't catch that joke, I'm a little horse).
If x/0 =0 then, since division is inverse of multiplication x= 0*0 this fails to hold for any x not 0
But the story says there is no defined multiplicative inverse of zero (undefined) so that they are free to choose any value they want. And they choose 0.
This is unsatisfactory to me because it seems to break the intuitive pattern of x/n getting larger as n approaches zero from the positives. 1/4 .25< 1/3 .33 < 1/2 .5 < 1/1 1 >1/0 0 >1/-1 -1 < 1/-2 -.5 < 1/-3 -.333
You see that sign flip thingy happening around 1/0?
Maybe I am misunderstanding.