I have a (computer science) homework assignment which has this snippet:
Treat the slope of a horizontal line segment as positive zero; treat the slope of a vertical line segment as positive infinity; treat the slope of a degenerate line segment (between a point and itself) as negative infinity.
I don't know what is a degenerate line segment, and what is the slope of that. I googled that but got very limited useful results.
Can someone explains to me what it is in simple terms?
Degeneracy in mathematics is not an exact term. For instance, a segment can be considered the degeneracy of a circle, an ellipse or even a triangle. So, the segment is a degenerate circle, a degenerate ellipse, or a degenerate triangle.
Another example is $0!$, which is a degenerate factorial whose value has to be defined because it is not given by the definition of $n!$. If we take a closer look, it will turn out that saying that $0!=1$ is very logical and useful, yet arbitrary at this level.
How to degenerate a segment then. As far as I can understand your problem, the point is considered to be a degeneracy of segments.
Since the slope is not defined for points, i.e. it is not defined for the said kind of degenerate segments, the author of the problem defines this concept. The following way:
Let the slope of the degenerate segment (the point) be defined as negative infinity.
Note that this definition is arbitrary. The author could define the slope of the degenerate segment as $\frac12$. There must be some unknown reason that makes the author's definition logical and useful.
The specification for this assignment now mentions the definition for a degenerate segment - a line segment between two same points.