Originally Posted by
Tim199
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.
But we're not talking about other analytics, we're talking specifically about the fuel mileage of a bicycle with respect to petroleum. It's a null and void concept from the get-go, because no petroleum is consumed in the act of pedaling a bicycle unless of course you are drinking it.
Originally Posted by
Tim199
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.
The link provided, in the comment to which I was replying, leads to a basic explanation of limits at infinite which is a building block concept of introductory calculus - I was making that reference and not implicating derivatives into the discussion.
The thing is, if g in your function is gallons consumed, as in (10mi travelled)/(gallons petrol consumed), then g is
always zero. g never existed from the start of this whole thing, which why the equation is always mi travelled/0g consumed. It's a linear trend with no slope, and no waxing analytical on the behavior of limits at infinity can change that. I once remarked that my bicycle got infinite mpg in that if I bought a gallon of gasoline it would sit the garage unused while I rack up miles on the bike...even this is erroneous because the metric mpg implies the petrol
consumed.