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Does 0.9999999 (repeating) Equal 1?

Okay, so yesterday I watched a video where this guy proposes a proof that 0.99999 (repeating to infinity) actually equals 1.  While his proof appears logical on the surface, it feels like utter nonsense.  Or to use real logic, anything based upon a falsehood is true.

Thinking about it, I decided that 0.99999 might be equal to 1.  Here's my logic:

0.9 = 0.3 x 3

0.3 x 3 = ⅓ x 3

⅓ x 3 = 1
Therefore,  0.9 = 1

What do you think?  Does this make sense?

Comments

  1. Yup, this is a correct proof that I was taught in high school. Hurt my brain at the time; now I'm more comfortable with it. =)

    ReplyDelete
    Replies
    1. I don't remember this from high school. But it almost hurts my brain now. :-D

      Delete

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