# Difference between half- line and ray

• Jan 10th 2012, 01:06 PM
Bashyboy
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?
• Jan 10th 2012, 01:56 PM
Plato
Re: Difference between half- line and ray
Quote:

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.
• Jan 10th 2012, 03:34 PM
Bacterius
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)
• Jan 10th 2012, 04:14 PM
Plato
Re: Difference between half- line and ray
Quote:

Originally Posted by 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.
• Jan 10th 2012, 04:43 PM
Bacterius
Re: Difference between half- line and ray
Quote:

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.

Quote:

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.
• Jan 10th 2012, 05:11 PM
Plato
Re: Difference between half- line and ray
Quote:

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 $\displaystyle \overrightarrow{PQ}=\overline{PQ}\cup\{X:P-Q-X\}$
• Jan 10th 2012, 05:22 PM
Bacterius
Re: Difference between half- line and ray
Quote:

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

Quote:

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.