y2-y1/x2-x1
the slope is infinite
Another riddle..
assuming x1,x2,y1,y2 are real numbers, this expression will either yield a real number or be undefined in the case of x1=x2, nothing with infinity.
Considering you are talking about a slope, you must be talking about a function. However, at no point has a function ever an infinite slope, even if the slope is approaching infinity.
I suspect the solution to this riddle is that you missed some brackets and where talking about a limit:
lim(x2->x1) (y2-y1)/(x2-x1)
This would be +∞ or -∞ depending on the orientation of x1,x2.
The brackets arent actually needed to create such limit, you could also have meant:
lim(x2->0) y2-y1/x2-x1
which would be +∞ or -∞ depending on if x2 comes from above or below.
I think this is unlikely though, as not only would y2 and x2 be utterly useless in this expression, but also because i think you cooked this one up by remembering the 5 minutes you were awake during math class, in which your teacher defined derivatives, which can be defined using a vaguely simular expression:
f'(a) = lim(x->a) (f(x)-f(a))/(x-a)
This would also explain why you were talking about a slope.
Either way, at best you only found another fancy way to express infinity - which is not a number
Edited 12/7/2023 06:10:21