Any line has an equation of y=mx+b. Now, if we take the m(x) (read here as the slope of line x) and -m(x) where x>0, we find that a the x axis is equidistant from both these lines.

Therefore, -m(x)<m(h)<m(x) and |m(h)-m(x)|=|m(h)+m(x)| from this we can conclude that the slope of a horizontal line has a slope of 0.

Now if we take a similar observation, that these lines are also equidistant from the y axis, we find that -m(x)>m(v)>m(x) and |m(v)-m(x)|=|m(v)+m(x)|. However, this is, as far as we know, impossible.

Now I have just defined undefined. Now we must find a way to place it on a number line. We can make a few observations to help us:

1) it is neither positive nor negative

2) it is not equal to zero

3) it is greater than positive and less than negative

We'll name the number numerical infinity

We can draw one of two conclusions from this:

1) the number line is, in fact, a misnomer. It is a circle such that 0 and numerical infinity cut the circle into two arcs. One arc represents the postive numbers, one the negative numbers.

2) I am wrong.