Originally Posted by
jfowler85
That is not irony, it's just bad math. Fuel mileage is calculated by the simple formula
(Miles traveled)/(gallons used)
which, for a bicycle which has traveled, say, 10 miles is
(10mi)/(0gal)
The problem here is that any number divided by zero is undefined. Ie it is not possible to divide something by nothing.
It's undefined in the sense that there is no real number that provides the desired solution, but that doesn't mean it can't be analyzed usefully at another level.
(Xmi)/(0gal) is not a derivative. The variable x is the mileage, and it is not approaching zero (think of a vector) and will never be anywhere near what could be construed as infinity; the fuel consumed is always zero. In other words, the graph is linear and not an asymptotic function, the plots only move in one direction from a singular point of origin 0,0.
It doesn't need to involve derivatives. Just because derivatives are defined with limits doesn't mean limits can't be considered separately. In your 10 miles travelled example, consider the function f=10/g. Then the right sided limit of f as g tends to zero is positive infinity. You can think of the mileage in whatever model you would like to, it's just probably not a good idea to refer to other people's math as bad when you don't have a strong handle on the mathematics involved and didn't appear to read the link that explained it.