You ever see a dog that’s got its leash tangled the long way round a table leg, and it just cannot grasp what the problem is or how to fix it? It can see all the components laid out in front of it, but it’s never going to make the connection.

Obviously some dog breeds are smarter than others, ditto individual dogs - but you get the concept.

Is there an equivalent for humans? What ridiculously simple concept would have aliens facetentacling as they see us stumble around and utterly fail to reason about it?

  • Lvxferre
    52·
    11 months ago

    Because it isn’t 0.9; it’s 0.999… with the ellipsis saying “repeat this to the infinite” being part of the number. And you don’t need to round it up to get 0.999… = 1, since the 9 keeps going on and on, so their difference is infinitesimally small = zero.

    Another thing showing that they’re the same number is that there is no number between them. For example:

    • 0.9 (no ellipsis) and 1 are different because 0.95 is between them
    • 0.95 and 1 are different because 0.97 is between them
    • there’s no number between 0.999… (with ellipsis) and 1, so they are the same. inb4 no “last nine” because it’s infinite.