is there a format math object ........

A vertex is a point in space.  A vector is a direction, but has no position.

Is there a formal mathematical object that contains both a vertex and a vector?  Lines aren't what I have in mind (those are defined by two vertices).  Right now in my program I'm just calling this construct a "bone" but that's a stupid word for it... is there a more formal terminology for a [Vertex, Vector] tuple?  "Directional point"?  Nah...

what are you using it for?

does your object have magnitude?  I can only imagine what you mean if you remove the magnitude part and only have direction.  Or perhaps it is a vector with two or more magnitudes, one magnitude for each of the dimensions of the space that it occupies.

yeah it sounds like whatever youre doing you could do with either a higher dimensional point containing directional information?  like >>3, it sounds to me youre talking about a point with direction, rather than a magnitude with direction, so it wouldn't be a vector.

or do you mean a vector that doesnt start at the origin?

also, if a point has a direction, that would imply that it can have an orientation.  now, if the point is the classical zero-dimensional thing, can it be assigned an orientation?  now I'm thinking of how a point on a curve can be assigned a slope value, though that idea has been in terms of the curve having a specific slope at a given point, rather than in terms of a point itself having a slope.

>>5
thats why derivitives are defined in terms of limits, since you would need a difference between two points to calculate slope.  the instantaneous slope is the value it approaches as that difference approaches 0.

perhaps all you really need to say is you have a zero-magnitude vector that is located at a specific point.  technically, it's still a vector, just that its magnitude equals zero.

>>7
the zero vector doesnt have direction though.  this is just some oriented point.

how do you orientate something with zero dimension?  There's no front or back to it.

A vertex is just 1 tomato of many. You, for instance, are a tomato.