616
Mind=Blown (lemmy.fmhy.ml)
submitted 3 years ago by to c/memes@lemmy.ml
67 comments fedilink hide all child comments
 
you are viewing a single comment's thread
view the rest of the comments
[–] 56 points 3 years ago* (2 children)

There is no difference, not even an infinitesimally small one. 1 and 0.999... represent the exact same number.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 4 child comments
    •
  • [–] 8 points 3 years ago (1 child)

    They only look different because 1/3 out of 1 can't be represented well in a decimal counting system.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 2 child comments
    •
  • [–] 5 points 3 years ago* (1 child)

    Right, it's only a problem because we chose base ten (a rather inconvenient number). If we did math in base twelve, 1/3 in base twelve would simply be 0.4. It doesn't repeat. Simply, then, 1/3 = 0.4, then (0.4 × 3) = (0.4 + 0.4 + 0.4) = 1 in base twelve. No issues, no limits, just clean simple addition. No more simple than how 0.5 + 0.5 = 1 in base ten.

    One problem in base twelve is that 1/5 does repeat, being about 0.2497.... repeating. But eh, who needs 5? So what, we have 5 fingers, big whoop, it's not that great of a number. 6 on the other hand, what an amazing number. I wish we had 6 fingers, that'd be great, and we would have evolved to use base twelve, a much better base!

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 2 child comments
    •
  • [–] 3 points 3 years ago* (last edited 3 years ago) (1 child)

    Well, technically “infinitesimally small” means zero sooooooooo

    Edit: this is wrong

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 2 child comments
    •
  • [–] 13 points 3 years ago (2 children)

    An infinitesimal is a non-zero number that is closer to zero than any real number. An infinitesimal is what would have to be between 0.999... and 1.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 4 child comments
    •
  • [–] 9 points 3 years ago (1 child)

    You are correct and I am wrong, I always assumed it to mean the same thing as a limit going to infinity that goes to 0

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 2 child comments
    •
  • [–] 8 points 3 years ago* (1 child)

    It's a weird concept and it's possible that I'm using it incorrectly, too - but the context at least is correct. :)

    Edit: I think I am using it incorrectly, actually, as in reality the difference is infinitesimally small. But the general idea I was trying to get across is that there is no real number between 0.999... and 1. :)

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 2 child comments
    •
  • [–] 2 points 3 years ago (1 child)

    I think you did use it right tho. It is a infinitesimal difference between 0.999 and 1.

    "Infinitesimal" means immeasurably or incalculably small, or taking on values arbitrarily close to but greater than zero.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 2 child comments
    •
  • [–] 5 points 3 years ago

    The difference between 0.999... and 1 is 0.

    It is possible to define a number system in which there are numbers infinitesimally less than 1, i.e. they are greater than every real number less than 1 (but are not equal to 1). But this has nothing to do with the standard definition of the expression "0.999...," which is defined as the limit of the sequence (0, 0.9, 0.99, 0.999, ...) and hence exactly equal to 1.

  • permalink
  • fedilink
  • source
  • parent