5 ms·

Doesn't a simple application of l'hospital solve this?

by alephNaught 15y ago

Rusky 15y ago
That's addressed in the article under "cleverest student."
- TrevorBurnham 15y ago
  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.
deleted 15y ago
[deleted]
webspiderus 15y ago
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 :)
- _delirium 15y ago
  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. See: http://en.wikipedia.org/wiki/Use_of_the_circumflex_in_French#Disappearance_of_.22s.22 http://en.wikipedia.org/wiki/Use_of_the_circumflex_in_French... and: http://en.wikipedia.org/wiki/Guillaume_de_l%27H%C3%B4pital#cite_note-0 http://en.wikipedia.org/wiki/Guillaume_de_l%27H%C3%B4pital#c...
  - webspiderus 15y ago
    ah, thanks - I had a feeling it was something like that! I figured a Calculus book would probably get it right :)
- tzs 15y ago
  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.
tzs 15y ago
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).
TrevorBurnham 15y ago
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.

Doesn't a simple application of l'hospital solve this?

Rusky 15y ago

That's addressed in the article under "cleverest student."

TrevorBurnham 15y ago
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.

deleted 15y ago

[deleted]

webspiderus 15y ago

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 :)

_delirium 15y ago
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. See: http://en.wikipedia.org/wiki/Use_of_the_circumflex_in_French#Disappearance_of_.22s.22 http://en.wikipedia.org/wiki/Use_of_the_circumflex_in_French... and: http://en.wikipedia.org/wiki/Guillaume_de_l%27H%C3%B4pital#cite_note-0 http://en.wikipedia.org/wiki/Guillaume_de_l%27H%C3%B4pital#c...
- webspiderus 15y ago
  ah, thanks - I had a feeling it was something like that! I figured a Calculus book would probably get it right :)
tzs 15y ago
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.

tzs 15y ago

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).

TrevorBurnham 15y ago

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.