Mathematics

I don't think "Gregorian" is an appropriate antonym to the astronomical practice of counting a day from noon to noon. After all the Julian day number is not named for Caesar either.

robjohn

I am used to using the JDN without regard to year start or end. EG it is now 2455927.528044

or it was a bit ago :-)

Henning Makholm

12:42 AM

Yeah, but floor(JDN) changes its value at noon.

robjohn

@HenningMakholm Indeed, that is what I meant in my first reply to your HNY comment.

Henning Makholm

Correcting myself: Wikipedia states that the Julian date is indeed named (indirectly) for Caesar -- in contrast to the popular myth that claims the correct explanation is a myth.

robjohn

@HenningMakholm I get dizzy just reading that.

@Henning: for some reason, which I am still trying to determine, Didier did not like my answer about Stirling. He has not replied to my most recent comment.

I think everything is in order, but perhaps there is some detail left out. However, I include more detail than Byron does.

I don't know for sure, but I think that Didier is the one who downvoted.

At least he is the only one to have raised an objection.

Time to walk the dog. Happy New Year to those whose meridian passes midnight before I return.

Henning Makholm

I'm afraid the answer is beyond the kind of analysis I know how to fake my way through.

robjohn

@HenningMakholm I will see what Didier says if he replies to my comment

Potato

1:09 AM

If I want to show L is a closed subspace of K, why does it suffice to show that every closed subset of L is closed in K?

The proof shows that every closed subset of L is closed in K, and that if A is closed in K, $A\cap L$ is closed in $L$. Why does this work?

Srivatsan

1:27 AM

Kannappan: What do you need this integral for? $\int_0^{\pi} {\dfrac{1-\cos mx}{1-\cos x}dx}$

Zhen Lin

2:25 AM

@Potato: Because L is a closed subset of L. :p

Potato

Yeah, actually he was going for the subspace topology, which is why I was confused.

Srivatsan

2:43 AM

Suggestions, criticisms welcome: math.stackexchange.com/a/95528/13425.

Henning Makholm

I haven't gotten to your answer yet, but there's an interesting misparse in the question: He wants to prove lim_{x->2} (x^3=8) -- not the correct (lim_{x->2} x^3)=8.

Srivatsan

I see =)

Henning Makholm

Also, the quantifier on x seems to be missing from his definition of limit, which can't be helping his understanding either.

Srivatsan

@HenningMakholm Perhaps the book is using the convention that missing quantifiers are universal.

Henning Makholm

Well, yes, but that doesn't tell us where in the quantifier hierarchy it should bind.

It's rather essential that the delta you produce must not depend on x.

On the other hand there are x's on both sides of the \Rightarrow, and these have to be bound by the same quantifier.

Srivatsan

2:52 AM

Oh, let me revise that: missing quantifiers are (a) universal, (b) placed in the innermost position.

I agree that the definition should make it explicit so that students are not confused, or worse yet, misled.

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$Mathematics$ Mathematics