• @[email protected]
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      131 year ago

      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.

      • @[email protected]
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        91 year ago

        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

        • @[email protected]
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          1 year ago

          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. :)

          • @[email protected]
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            21 year ago

            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.

            • Kogasa
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              51 year 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.

      • Ghoelian
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        21 year ago

        Wait what

        I always thought infinitesimal was one of those fake words, like gazillion or something

        • @[email protected]
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          31 year ago

          It sounds like it should be, but it’s actually a real (or, non-real, I suppose, in mathematical terms) thing! :)