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Thread: Absolute Values

  1. #1
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    Absolute Values

    The distance between a and n is |a - b| = |b - a|.

    Using the definition given above, rewrite the statement using absolute value.

    The distance between x^3 and -1 is at most 0.001.

    The distance between x^3 and -1 is | x^3 + 1|.

    The |x^3 + 1| is at most 0.001 can be expressed as

    |x^3 + 1| is < or = 0.001.

    Question:

    Why must we set |x^3 + 1| to be less than or equal to 0.001and not greater than or equal to 0.001?
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  2. #2
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    Re: Absolute Values

    review the definitions of "at least" and "at most"
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    Re: Absolute Values

    Quote Originally Posted by mathdad1965 View Post
    Why must we set |x^3 + 1| to be less than or equal to 0.001and not greater than or equal to 0.001?
    The statement $|x^3+1|\ge 0.001$ means that the distance from $x^3$ to $-1$ is at least $0.001$.
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    Re: Absolute Values

    Correction:

    In the definition given, n should be b.

    The distance between a and b is |a - b| = |b - a|.
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    Re: Absolute Values

    Quote Originally Posted by romsek View Post
    review the definitions of "at least" and "at most"
    The textbook is not too clear on the AT LEAST AND AT MOST definitions.

    1. Can you provide a simple explanation?

    2. In what way is the concept of AT LEAST AND AT MOST related to the number line?
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    Re: Absolute Values

    Quote Originally Posted by mathdad1965 View Post
    The textbook is not too clear on the AT LEAST AND AT MOST definitions.

    1. Can you provide a simple explanation?

    2. In what way is the concept of AT LEAST AND AT MOST related to the number line?
    $x \text{ is at least } a \text { if } a \leq x$

    $x \text { is at most } a \text{ if } x \leq a$

    with regard to the number line.

    $\text{ if } x \text{ is at least } a \text{, then } x \in [a , \infty)$

    $\text{ if } x \text{ is at most } a \text{, then } x \in (-\infty, a]$
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    Re: Absolute Values

    Quote Originally Posted by romsek View Post
    $x \text{ is at least } a \text { if } a \leq x$

    $x \text { is at most } a \text{ if } x \leq a$

    with regard to the number line.

    $\text{ if } x \text{ is at least } a \text{, then } x \in [a , \infty)$

    $\text{ if } x \text{ is at most } a \text{, then } x \in (-\infty, a]$
    You said in your most recent reply that
    x is at least a if a is less than or equal to x.
    Shouldn't it be if a is greater than or equal to x?
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    Re: Absolute Values

    Quote Originally Posted by mathdad1965 View Post
    You said in your most recent reply that
    x is at least a if a is less than or equal to x.
    Shouldn't it be if a is greater than or equal to x?
    no

    x is at least a means $x \geq a$

    x is a or larger
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    Re: Absolute Values

    Quote Originally Posted by romsek View Post
    no

    x is at least a means $x \geq a$

    x is a or larger
    Your inequality symbol is correct now but not in the previous reply. See it?
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    Re: Absolute Values

    Note: x is at least a means that x > or = to a not x < or = to a. Correct?
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    Re: Absolute Values

    Quote Originally Posted by mathdad1965 View Post
    Note: x is at least a means that x > or = to a not x < or = to a. Correct?
    it's correct in both. Take another look.
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    Re: Absolute Values

    Quote Originally Posted by romsek View Post
    it's correct in both. Take another look.
    Thank you for your input.
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