4 ms·

We have... in a sense. There are number systems wherein 0 is treated rather like dx in terms of being a formal entity upon which algebraic manipulations can be

We have... in a sense. There are number systems wherein 0 is treated rather like dx in terms of being a formal entity upon which algebraic manipulations can be performed; in such systems we can say for example that sin(0)/0 = 1 while sin(0^2)/0 = 0.

tprice7 9y ago
Do you have a reference for this? I would believe you if you said "an infinitesimally small value" rather than 0. If it's true then I'm very surprised. For one, 0 = -0, so if sin(0)/0 = 1, then -1 = -sin(0)/0 = sin(0)/-0 = sin(0)/0 = 1
- cperciva 9y ago
  I'm talking about various forms of infinitesimals, yes. In a sense they're zero, but in another sense they're not. For the reasons you mention, these models have 0 != -0. :-)
  - tprice7 9y ago
    But don't these models all have a true zero, distinct from the infinitesimals, which is its own negative?
    - cperciva 9y ago
      Usually, yes. But sometimes it's written as 0^\infty.
      - tprice7 9y ago
        "Usually" So there is an instance where this isn't the case?
        cperciva 9y ago
        Well... notation. People come up with all sorts of ways of writing things and all sorts of weird models.