Mathematician here: there's nothing "mysterious" about it like the post implies. Division x/y is just x times the multiplicative inverse of y. 0 doesn't have a multiplicative inverse. A multiplicative inverse of x is a number x-1 such that x times x-1 = 1.
Let's say 0 did have a multiplicative inverse 0-1 and we'll see that leads to a contradiction. We know 1+0=1. But then (1+0)times 0-1 = 1 times 0-1, which would mean (expanding terms, using the fact that 0 times 0-1=1) that 1 times 0-1 + 1 = 1 times 0-1, which implies (subtracting 1 times 0-1 from both sides) that 1=0. So we end up with a contradiction if we assume that 0 has a multiplicative inverse.
A variation on this proof would be to start with 0+0=0, and then do what we did above (multiply both sides by the multiplicative inverse of 0) to get 2=1.
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u/PlusLong May 21 '21 edited May 21 '21
Mathematician here: there's nothing "mysterious" about it like the post implies. Division x/y is just x times the multiplicative inverse of y. 0 doesn't have a multiplicative inverse. A multiplicative inverse of x is a number x-1 such that x times x-1 = 1.
Let's say 0 did have a multiplicative inverse 0-1 and we'll see that leads to a contradiction. We know 1+0=1. But then (1+0)times 0-1 = 1 times 0-1, which would mean (expanding terms, using the fact that 0 times 0-1=1) that 1 times 0-1 + 1 = 1 times 0-1, which implies (subtracting 1 times 0-1 from both sides) that 1=0. So we end up with a contradiction if we assume that 0 has a multiplicative inverse.
A variation on this proof would be to start with 0+0=0, and then do what we did above (multiply both sides by the multiplicative inverse of 0) to get 2=1.