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While these proofs are quite convincing there is one observation that has been ignored in the above proofs. If you divide any number by 9 you get the pattern. For example 5/9 = 0.55555555……till infinity. So 9 * 0.55555555….. = 5. In same way if we divide 9/9 we get 1 as quotient. But as per the pattern observed it should be 0.99999999…..till infinity. So we can say that 0.999999999….. = 1.

Hello Vi Hart.

x = .222222….

10 x = 2.22222222222.

10 x – x = 2

9x = 2

x = 2/9

I agree that in the context of the super infinity,

that .9999999999999999… is infinitesimally < 1.

The set of real numbers is defined exactly to exclude infinitesimals.

It is only because .0000000000000000….1

is not deemed to be a real number,

that we must identify .999999999999999 with 1.

.0000000000000000….1 can be considered to be a unit infinitesimal in

an enlarged arithmetic beyond the real number system.

Kermit

Hi, Kermit,

If you want to chat with Vi, you might try visiting her blog.

Hello Denise, Could you please put your stand about 0.99999999…. = 1 ?

As far as everyday mathematics is concerned, 0.999…=1. Definitely. This video was an April Fool’s Day post.

If there are strange branches of math in which 0.999… is not one, or in which you can divide by zero or do other funky things, I know nothing about those. I’m just a homeschool teacher. You can ask Vi about math like that by posting a comment on her blog or YouTube channel.