Recent content by jaqueh

Homework Statement There are exactly 33 postage amounts that cannot be made up using these stamps, including 46 cents. What are the values of the remaining stamps? Homework Equations stamp 1 = x stamp 2 = y Im assuming postage amounts range from 1 to 100 cents The Attempt at a...

Homework Statement Suppose p is a prime number. Prove that p is irreducible in Z[√−5] if and only if there does not exist α ∈ Z[√−5] such that N(α) = p. Using this, find the smallest prime number that is not irreducible in Z[√−5]. Homework Equations α = a+b√−5 ∈ Z[√−5] N(α) = a2 + 5b2...

sorry i meant for the interval to be [0,2] then i get f(0)=f(2)=0 => rolle's

I got it, make [0,1] a subset of [-1,3] then i can use Rolle's theorem and then determine that there must be a c in [0,1] so there's got to be a c in [-1,3]

Homework Statement Show f(x)=(x−2)sinxln(x+2) has f'(x)=0 somewhere on [-1,3] The Attempt at a Solution I tried using Rolle's theorem, but f(-1)≠f(3). Then I tried the mean value theorem, but didn't get 0 either.

ok I think I get what I can do now with the polygon ineq. except I thought that it would only be less than 2-n+...+2m-1also I don't know if I need to prove the polygon identity or not. if I did how would I go about it? would I use a fact of geometric series?

Homework Statement Suppose the sequence (Sn) is defined as: |Sn+1-Sn|<2-n show that this is a cauchy sequence Homework Equations hint: prove the polygon identity such that d(Sn,Sm)≤d(Sn,Sn+1)+d(Sn+1,Sn+2)...+d(Sm-1,Sm) The Attempt at a Solution I have defined Sm and Sn and created the...

ok great I have it now. I do that then squeeze because I'm not allowed to say yet that 1/n goes to zero in a sequence I think

ah I've divided the numerator by 3 but am still stuck. I know it hits -3. yeah I'm trying to see what I can make the expression into so things will start cancellong

Homework Statement limit of the sequence, [xn]=(-3n2+n+1)/(n2-2n+3) Homework Equations I so far know about the definition of a limit, squeeze principle, and lim[xnyn] = 0 if xn or yn goes to 0 The Attempt at a Solution Tried the definition of the limit but the algebra got really...

yeah i realized that, what i have on my paper is just that q is in the set which implies b is not a sup

oh ok, thanks for pointing that out i would have gotten that wrong on the assignment :-p

no i understood the pi example, but a is defined to be greater than all elements of the set in the definition. i guess the only thing that's important is that it's the lowest

got it rough pf- Suppose all the stuff in the question i) a is a maximum because of the nature of the set. ii) suppose not, suppose there's a 'b' such that sup(e)=b so b<a. Then the interval b<a is dense so that b<q<a for some rational q. Therefore this implies that b is in the set and that...

ok i will try that, i know the traditional way of proving a supremum, just this one throws me for a loop because its rationals and irrationals