What is the difference between 1 and 0.999…?

Which is bigger do you think?

Hello guys I’m Yuya and I major in mathematics. Have you ever wondered about it? It’s a very popular issue in the math world. Do you think 1 is bigger? Is that true? I’ll try to explain this to you.

First we define x = 0.999…  . And we multiply x by 10x = 9.9999…. It means: 10x-x. Is it OK? Let’s compare x = 0.999… with 10x = 9.999….

It’s true. I’ll deduct x = 0.999… from 10x = 9.999…. : it means 10x-x.

It will be x = 1. Do you understand the above equation?

However, we defined x = 0.999…

So it will be 1 = 0.999…

They don’t have difference in the math world. Are you interested in mathematics?

Yuya Yamaguchi, Intermediate B

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2 thoughts on “What is the difference between 1 and 0.999…?

  1. I am so interested in your article!!
    According to your article, there are no difference between 1,000……….1 and 1.But how can we prove it?
    I think there are a lot of questions in the world and that makes the world interesting.

  2. Hi, I’ m Mizuki. Your article was really attractive to me! I liked math the same as English when I was a high school student, so your post reminded me of that.
    Is their really a difference between 0.999… and 1? I want to know that very much!

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