Memes

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[–] KoboldCoterie@pawb.social 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.

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[–] fahfahfahfah@lemmy.billiam.net 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

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[–] KoboldCoterie@pawb.social 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. :)

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[–] LegendofZelda64@lemmy.fmhy.ml 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.

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[–] kogasa@programming.dev 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.

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[–] Ghoelian@feddit.nl 2 points 3 years ago (1 child)

Wait what

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

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[–] KoboldCoterie@pawb.social 3 points 3 years ago

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