• Shampiss@sh.itjust.works
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    9 months ago

    Divide 1 by 3: 1÷3=0.3333…

    Multiply the result by 3 reverting the operation: 0.3333… x 3 = 0.9999… or just 1

    0.9999… = 1

    • ArchAengelus@lemmy.dbzer0.com
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      9 months ago

      In this context, yes, because of the cancellation on the fractions when you recover.

      1/3 x 3 = 1

      I would say without the context, there is an infinitesimal difference. The approximation solution above essentially ignores the problem which is more of a functional flaw in base 10 than a real number theory issue

      • Shampiss@sh.itjust.works
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        9 months ago

        The context doesn’t make a difference

        In base 10 --> 1/3 is 0.333…

        In base 12 --> 1/3 is 0.4

        But they’re both the same number.

        Base 10 simply is not capable of displaying it in a concise format. We could say that this is a notation issue. No notation is perfect. Base 10 has some confusing implications

        • ColeSloth@discuss.tchncs.de
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          9 months ago

          They’re different numbers. Base 10 isn’t perfect and can’t do everything just right, so you end up with irrational numbers that go on forever, sometimes.

    • ColeSloth@discuss.tchncs.de
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      9 months ago

      You’re just rounding up an irrational number. You have a non terminating, non repeating number, that will go on forever, because it can never actually get up to its whole value.

      • WldFyre@lemm.ee
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        9 months ago

        1/3 is a rational number, because it can be depicted by a ratio of two integers. You clearly don’t know what you’re talking about, you’re getting basic algebra level facts wrong. Maybe take a hint and read some real math instead of relying on your bad intuition.

        • ColeSloth@discuss.tchncs.de
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          9 months ago

          1/3 is rational.

          .3333… is not. You can’t treat fractions the same as our base 10 number system. They don’t all have direct conversions. Hence, why you can have a perfect fraction of a third, but not a perfect 1/3 written out in base 10.

          • WldFyre@lemm.ee
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            9 months ago

            0.333… exactly equals 1/3 in base 10. What you are saying is factually incorrect and literally nonsense. You learn this in high school level math classes. Link literally any source that supports your position.

          • pyre@lemmy.world
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            9 months ago

            .333… is rational.

            at least we finally found your problem: you don’t know what rational and irrational mean. the clue is in the name.

            • Klear@sh.itjust.works
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              9 months ago

              TBH the name is a bit misleading. Same for “real” numbers. And oh so much more so for “normal numbers”.

              • pyre@lemmy.world
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                9 months ago

                not really. i get it because we use rational to mean logical, but that’s not what it means here. yeah, real and normal are stupid names but rational numbers are numbers that can be represented as a ratio of two numbers. i think it’s pretty good.