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?

Re: Difference between half- line and ray

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Originally Posted by

**Bashyboy** 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 $\displaystyle A~\&~B$ the ray $\displaystyle \overrightarrow{AB}=\overline{AB}\cup\{X:A-B-X\}.$

Whereas the half-line $\displaystyle \overrightarrow{AB}\setminus\{A\}$.

In other words, a half-line is a ray without its endpoint.

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 (Wondering)

Re: Difference between half- line and ray

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**Bacterius** 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 (Wondering)

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.

Re: Difference between half- line and ray

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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.

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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.

Re: Difference between half- line and ray

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Originally Posted by

**Bacterius** 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 $\displaystyle P~\&~Q$ are two points then $\displaystyle \overrightarrow{PQ}=\overline{PQ}\cup\{X:P-Q-X\}$

Re: Difference between half- line and ray

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You have a problem with mathematical vocabulary don't you?

You don't have to become aggressive and condescending.

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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.