Recent content by redone632

Hmm, I never really thought of it like that. So my original answer was correct? (1C1 * 8C3) / 9C4

I don't understand why you chose 4C1 and 5C3. The way I thought of it was just like any other Hypergeometric problem. For example, you have a bag of 9 marbles, 1 black and 8 white. What is the probably that you will get the black marble when you pick 4 marbles without replacement. So there is 1...

Homework Statement Suppose 9 mice are available for a study of a possible carcinogen and 4 of them will form a control group (i.e. will not receive the substance). Assuming that a random sample of 4 mice are selected, what is the probability that a particular mouse, Mike Mouse will be included...

That's what I thought. We've just been dealing with defining epsilon so much I want to be sure. I'll go over my notes to see if I can come up with something. Thanks!

Alright, but how do I go about defining my epsilons to be?

Homework Statement Let K be a compact sebset of a metric space (X, d) and let \epsilon greater than 0. Prove that there exists finitely many points x_1 x_2, ... x_n \in K such that K is a subset of the union of the \epsilon neighborhoods about x_i Homework Equations N/A The Attempt...

Hmmm, I think I've made some development but I'm still unsure how solid it is. Let E be an open subset of \Real. Define the equivalence relation x \sim y \Longleftrightarrow \exists (a,b) such that {x,y} \in (a,b) \subseteq E. The equivalence classes will be distinct. By the archimedean...

Homework Statement Prove that any open subset of \Real can be written as an at most countable union of disjoint open intervals. Homework Equations An at most countable set is either finite or infinitely countable. The Attempt at a Solution It seems very intuitive but I am at lost...

Oh wow, I swear I miss the most obvious things. Thanks for your help again!

Since H is a subgroup of order m, xHx^(-1) will be a subgroup of order m. Since H is the only subgroup of order m there will be no other subgroup such that xKx^(-1) is of order m. Therefore, xHx^(-1) = H. I think that's it, but I can't connect the dots to the last statement.

Homework Statement Let G be a finite group and H a subgroup of G having order m. Show that if H is the only subgroup of order m in G, then H is normal in G. Homework Equations A subgroup H of G is normal in G if and only if xHx^{-1} \subseteq H \forall x \in G The Attempt at a...

Awesome. Thanks!

Hmmm I think I got it. I just want to make sure it's right. Since 2, 5, 7 are primes that divide 70. Then by Cauchy's Theorem there must be an elements of order 2, 5, 7 say, a, b, c respectively. Since G is abelian, then every subgroup must be normal. Therefore, the subgroups generated a, b, c...

Homework Statement Show that every abelian group of order 70 is cyclic.Homework Equations Cannot use the Fundamental Theorem of Finite Abelian Groups.The Attempt at a Solution I've tried to prove the contrapositive and suppose that it is not cyclic then it cannot be abelian. But that has lead...