Science Memes

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I just cited myself. (mander.xyz)

submitted 9 months ago by [email protected] to c/[email protected]

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[–] [email protected] 6 points 9 months ago (2 children)

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

[–] [email protected] 25 points 9 months ago* (last edited 9 months ago) (1 children)

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

[–] [email protected] 1 points 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.

[–] [email protected] 10 points 9 months ago

This seems to be conflating 0.333...3 with 0.333... One is infinitesimally close to 1/3, the other is a decimal representation of 1/3. Indeed, if 1-0.999... resulted in anything other than 0, that would necessarily be a number with more significant digits than 0.999... which would mean that the ... failed to be an infinite repetition.