Recent content by Bacle

Sazanda: The definition you gave is the same as that of totally-bounded. I mean, totally.

Hi, All: How do I change the e-mail to which replies/followups were previously sent to me?

What is your definition ofS being precompact? The one I knew is that the closure of S is compact.

nyr: Assume for a moment that the difference xn-yn is always positive, or nonnegative. What can you then say about Limn→∞|xn-yn|? Consider then all other possible cases re the difference xn-yn

Haven't looked at it carefully, but slope should be -1.5, after substitution.

Fluidistic: Just thought I'd give DreamLord something to think about in case of being accepted to both an Ivy with low funding and a non-Ivy with higher funding. Is the extra $'000's of debt seriously worth the Ivy degree? Still, like I said, if you get good funding for an Ivy, go for it...

I'm not sure, but if it is any consolation, according to the book "Higher Education?", those who graduate (at least in undergraduate) from an Ivy-League school , or some other top-10, do not, on average, do better down the road, after, say, 10 years, than those with a degree from a state...

So, to be more specific: Let L be the linear map L:R3→R3represented by M, with : M=[ 0 1 0] [ 0 0 1] [ 0 0 0] Then the kernel of M is the subspace spanned by {(x,0,0)}, i.e., if we have the standard xyz-axes, then the entire line is crushed to 0. Now, M2= [ 0 0 1] [ 0...

But there cannot be a continuous surjection , because the circle is compact, and the interval [0,1) is not, so f(S1)=[a,b], since the compact subsets of the real line are the closed+bounded intervals, and f continuous maps compact to compact.

Thanks, that was helpful. From what I remember, there are no comments in the label re adding nutrients, nor changing anything, but I'll check next time.

Tazz01: I may be missing something, maybe even something obvious, but I think that given _any_ linear transformation L from R3 to R3, we can find a decomposition as in i), but it is not true for _every map_ L as above that kerL=KerL2. As example, take a linear map L , whose matrix...

BTW, ignore my previous post; I misread the OP, sorry. Re #1: No, read carefully: F'(1) is the rate of change of the rain _at t=1_

But what's confusing is that the set {1,1,2,5} is the same as {1,2,5}, by basic set properties. One way of understanding the product of a set by an interval is by considering a subset of the product of 2 intervals, say , the interval [1,5], and [1,2] , then {1,2,5}x [1,2] will just...

If T is a linear transformation, T(a+b)=T(a)+T(b), and 0=0+0... Still, unless I am missing something in your notation or otherwise, I think there are counterexamples: For any T:R3→ R3, we have the decomposition in i) by, say, choosing a basis for R3, and representing T using a...

How can F'(2) be smaller than F'(1)?