> There is a duality between zero and infinity, expressed in the elementary identity 1/0 = ∞.
I understand what they're saying here - but I was always under the impression that, rather than yielding infinity, division by zero was undefined. Wikipedia [1] says that this is true "In ordinary arithmetic", but goes on to say that it is "sometimes useful" to think of a "formal calculation" involving division by zero as evaluating to infinity. A formal calculation seems to be one that ignores whether the result is well defined.
Would anyone care to comment on whether the mathematical perspective above carries over into the physics domain?
> There is a duality between zero and infinity, expressed in the elementary identity 1/0 = ∞.
I understand what they're saying here - but I was always under the impression that, rather than yielding infinity, division by zero was undefined. Wikipedia [1] says that this is true "In ordinary arithmetic", but goes on to say that it is "sometimes useful" to think of a "formal calculation" involving division by zero as evaluating to infinity. A formal calculation seems to be one that ignores whether the result is well defined.
Would anyone care to comment on whether the mathematical perspective above carries over into the physics domain?
[1] https://en.wikipedia.org/wiki/Division_by_zero