Gradient of x=something e.g vertical line

[Joe2]

I was just curious if there was a solution to the gradient of x = 0, i was thinking it must be infinity but wasn't sure and was wondering if there was a definite answer or if it was one of many unsolved problems.

 

[Dr.Peterson]

I was just curious if there was a solution to the gradient of x = 0, i was thinking it must be infinity but wasn't sure and was wondering if there was a definite answer or if it was one of many unsolved problems.

It could be thought of, informally, as "infinite", but properly speaking it is undefined. That's because it would require dividing by zero (the change in x between any two points on the line), and that can't be done. That is, it's impossible even to define what 1/0 would mean; 0 times any number is still 0. Infinity is not a number.