0.999...= 1 - Hackdot

Re:0.999...= 1 by jdoliner on Tuesday April 28, 2020 @11:37AM (#23008035)

When I was a child I was convinced by a pretty simple conversation with my father:

Me: 0.9999... is not the same as 1

Him: Well if it's not the same is it more than 1 or less than 1?

Me: Less

Him: Okay then how much less is it?

At this point I started trying to do 1 - 0.999..., using the methods I'd been taught, and after a few iterations of "borrowing" the 1 I realized the answer was 0.000... which I was pretty convinced was equal to 0.

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Re:0.999...= 1 by hota_mazi on Tuesday April 28, 2020 @11:41AM (#23008091)

Hehe... smart man.

Another one is that

1 / 3 * 3 = 1

<==> 0.333... * 3 = 1

<==> 0.999... = 1

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Re:0.999...= 1 by umvi on Tuesday April 28, 2020 @11:45AM (#23008125)

"yes but 1/3 does not equal .333... it's just an approximation since there's no perfect way to represent 1/3"

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Re:0.999...= 1 by jdoliner on Tuesday April 28, 2020 @12:58PM (#23008987)

If 1/3 doesn't equal .333... then how much do they differ by?

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Re:0.999...= 1 by brutt on Tuesday April 28, 2020 @01:04PM (#23009054)

    (1/3)/∞

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Re:0.999...= 1 by brutt on Tuesday April 28, 2020 @12:58PM (#23008984)

In base 3,

    1/10*10=1, 0.1*10=1

What the problem?

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