Math is crazy: 1 = 0.9999…

There’s no difference between the number 1 and the seemingly smaller number 0.9999… (with 9 repeating endlessly). I used to think that there must be some tiny but key difference, but it turns out there just isn’t any. They seem different and are written differently, but they are the same.

Here’s one proof: Multiply 0.999999… by 10.

That’s 9.999999…

Then subtract 0.999999…

The result is 9.

What’s the difference between ten and nine?  One.

It’s true that the solution for 10x-x=9 is 1.

So 0.9999… = 1.  Weird!


5 thoughts on “Math is crazy: 1 = 0.9999…

  1. Alright man, I am a fan of the mathematics. This is pretty interesting in the fact that it is similar to an idea I have had but am more or less afraid to put it down;

    1 is infinitely more than 0 and 0 is nothing. Therefore, 1 is everything.

    I feel like this is crazy talk, but so is math. What do you think?

  2. Definitely crazy talk, but it’s the kind I like.
    I can’t say what I think yet. What does “therefore, 1 is everything” mean?
    All the different possible meanings I can think of make me go, “…duuuude.”

  3. Your math is wrong 0.999999999*10=9.99999999
    9.99999999-0.999999999=8.999999991 (not 9)
    It’s true that the solution for 10x-x=9 is 1
    but 0.999999999 is not a solution for this eq.

    • 9.9-.9 is 9.

      9.99-.99 is 9.

      9.999-.999 is 9.

      At what point in this sequence is the result less than 9?

      • 9.9-0.99=8.91 (0.99*10=9.9)
        As in the 1st line of the “proof” says “Multiply 0.999999… by 10.”,the first number must be 10 times the second number (10x-x=9).

        9.99-0.999=8.991 (0.999*10=9.99)

        9.999-0.9999=8.9991 (0.9999*10=9.999)

        So always is less than 9.

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