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A ray looks like:

------->

A 2D analoge would look like:

^
|
|
|
----------->

Is there a name for this in higher than one-dimension?

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  • $\begingroup$ quarter plane is my guess $\endgroup$
    – Integrand
    May 13, 2021 at 22:41
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    $\begingroup$ I would say either cone / convex cone, depending on whether you want to include the area between the two rays. $\endgroup$
    – Rushy
    May 13, 2021 at 22:41

1 Answer 1

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In my opinion, the generalization of a ray in a $n$-dimensional real vector space could start by defining a ray as all the linear combinations of the basis vectors such that all coefficients intervening in the sum have the same sign. Under this logic, a 2D ray in the cartesian plane would consist in a section of the latter lying between (and including) two non-colinear vectors.

This is, imagine a pizza slice that can be almost as wide as half the plane, or almost as thin as the 1D ray.

All this, though, cannot really be considered an answer, but rather a possible way of generalising the 1D ray, the way I would personally do it.

EDIT

As @Blue has commented, the definition above corresponds to the one of a convex cone, that @Rushy proposed earlier.

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    $\begingroup$ "In my opinion, the generalization of a ray in a $n$-dimensional real vector space could start by defining a ray as all the linear combinations of the basis vectors such that all coefficients intervening in the sum have the same sign." You're not alone in this opinion. That's the definition of a "convex cone". $\endgroup$
    – Blue
    May 13, 2021 at 23:36
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    $\begingroup$ Wow, I feel kind of satisfied the object I was imaging is actually an already named mathematical object. Thank you for the information, I'll add it. $\endgroup$
    – Albert
    May 14, 2021 at 8:25

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