Thanks for the link to this. Very cool! While the OP describes a crowd-sourced solution, this seems to be a setup where 1 GPS is attached per vehicle.
On seeing this, I have a reaction that I'd like to share. Someone at this University had vision. They seem to have less than 20 buses in their fleet. However, we're still talking about a serious investment (It isn't just the phones, it is also data plans. They might be using their campus wifi network which would significantly lower their costs).
I've tried doing this in other places some time ago. However, it was impossible to get anyone to invest in such a thing. What do you do when you are in this situation? I've done mock-ups, buying initial hardware with my own $$, but still. I guess in our society, pretty much everything comes down to economic value. On one hand, it makes sense. On the other, it makes me sad. </rant>
This is completely off-topic, but did you mean to call it l'hospital as opposed to L'Hôpital? I remember even my calculus book had similar errors, and I always wondered if it was just because the two looked so similar (or if there was any more reasoning behind it). didn't mean to nitpick, your comment just triggered a repressed train of thought :)
His original name was actually Guillaume de l'Hospital; French spelling reforms later did away with a number of cases of silent 's' (which had been silent for a long time already), replacing it with a circumflex over the preceding vowel.
It's not an error. The french changed their spelling to replace a silent 's' after some letters with a circumflex over those letters. Using the silent s instead of a circumflex is considered correct when transcribing into English.
No. What would you apply it to in 0^0? The best you could do is come up with two functions, f(x) and g(x), with f(x) and g(x) going to 0 as x goes to 0, and try to use it to evaluate f(x)^g(x), but the result is going to depend on exactly what your choices are for f(x) and g(x).
A precondition of L'Hôpital's Rule is that the limit in question exists. So: Prove that the limit exists, and then you can bust out L'Hôpital's Rule to prove that it's 1.
And the cleverest student turns out to be right, given the convention asserted by the mathematician. If 0⁰ were 0, or indeterminate, then the limit wouldn't exist and, therefore, L'Hôpital's Rule wouldn't apply. But given that it's 1, the limit does exist, and all is well until Zermelo-Fraenkel is proven inconsistent.
