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Math Help - Difference between half- line and ray

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    Difference between half- line and ray

    My geometry book asks me to distinguish the two terms. First, though, I noted that you cannot have a half of a line becuase lines stretch indefinitely, isn't that correct? If so, did they possible mean segment? Because in that case, the half of a line segment would be a midpoint, and therein would the lie the distinction, that the midpoint is not a vertex. Am i mistaken, or missing anything? Or are my thoughts utterly wrong?
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    Re: Difference between half- line and ray

    Quote Originally Posted by Bashyboy View Post
    My geometry book asks me to distinguish the two terms. First, though, I noted that you cannot have a half of a line becuase lines stretch indefinitely, isn't that correct? If so, did they possible mean segment? Because in that case, the half of a line segment would be a midpoint, and therein would the lie the distinction, that the midpoint is not a vertex. Am i mistaken, or missing anything? Or are my thoughts utterly wrong?
    Infinity has nothing to do with these concepts.
    Given two points A~\&~B the ray \overrightarrow{AB}=\overline{AB}\cup\{X:A-B-X\}.
    Whereas the half-line \overrightarrow{AB}\setminus\{A\}.
    In other words, a half-line is a ray without its endpoint.
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    Super Member Bacterius's Avatar
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    Re: Difference between half- line and ray

    I always thought a ray had no endpoint (just a point, and a direction), therefore a half-line and a ray are two functionally equivalent terms. I might be wrong but then everything I find online seems to support this definition of a ray
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    Re: Difference between half- line and ray

    Quote Originally Posted by Bacterius View Post
    I always thought a ray had no endpoint (just a point, and a direction), therefore a half-line and a ray are two functionally equivalent terms. I might be wrong but then everything I find online seems to support this definition of a ray
    You have confused a vector with a ray.
    Have you ever studied Axiomatic Geometry ?
    The foundations of modern geometry are due to David Hilbert, G.H. Moore, & R.L. Moore.
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    Super Member Bacterius's Avatar
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    Re: Difference between half- line and ray

    You have confused a vector with a ray.
    How so? A vector has no position (origin) whereas a ray does. That would be the distinction between the two.

    Have you ever studied Axiomatic Geometry ?
    The foundations of modern geometry are due to David Hilbert, G.H. Moore, & R.L. Moore.
    No I haven't, I'll have a look.
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    Re: Difference between half- line and ray

    Quote Originally Posted by Bacterius View Post
    How so? A vector has no position (origin) whereas a ray does. That would be the distinction between the two.
    No I haven't, I'll have a look.
    You have a problem with mathematical vocabulary don't you?
    A vector is a scientific concept. A vector has length and direction.
    That is not a mathematical concept. Direction is not mathematical.

    On the other hand, axiomatic geometry is purely synthetic.
    If P~\&~Q are two points then \overrightarrow{PQ}=\overline{PQ}\cup\{X:P-Q-X\}
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    Super Member Bacterius's Avatar
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    Re: Difference between half- line and ray

    You have a problem with mathematical vocabulary don't you?
    You don't have to become aggressive and condescending.

    A vector is a scientific concept. A vector has length and direction.
    That is not a mathematical concept. Direction is not mathematical.
    What I meant is that a vector is that, a vector, whereas a ray is defined by a point and a vector (which would represent its "direction"). So a ray cannot be equivalent to a vector, thus my question of why I would have confused the notion of a ray and a vector.
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