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Thread: A recurring decimal and a parabola, how can they coincide?

  1. #1
    Oct 2012

    Question Parabola Problem!

    I am a high school student in the UK and have a mathematical problem i cannot get my head around.

    It has been explained to me that 0.999... recurring equals 1.
    It has also been explained that the gradient on a parabola will never be vertical.

    If 0.999... can 'touch' 1 and equal 1

    and the gradient of a parabola will get closer and closer to being vertical but never vertical

    Is there a relationship between a decimal that gets closer and closer to 1, in that 0.999 is closer to 1 than 0.9 and that a parabola's gradient gets closer and closer to vertical?
    And if 0.999.. recurring can equal 1 then why can't a parabola's gradient also be vertical?

    Say you had the line y=0.999 and the y intercept is 0.999.
    If you had the line y=0.999... recurring, the y intercept would be 0.999... recurring. So if you zoomed in and zoomed in on the graph, the y intercept would never be 1?

    Last edited by stuarttherock; Oct 29th 2012 at 08:20 AM.
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  2. #2
    MHF Contributor
    Sep 2012
    Washington DC USA

    Re: Parabola Problem!

    ".999..." is a symbol. The number that symbol represents is 1. That number *is* the number 1. They are the same. They are **EQUAL**!!
    I don't think there's anything about that that's obviously comparable to a parabola's steepness (slope), which is always simply a well defined number at every point on the parabola.
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