Recent content by Mathnerdmo

(1) looks good. In (2), your answer is correct, but all you've shown is a subgroup with the same order as Z9⊕Z4. Being isomorphic is much stronger than having the same order, though, so you're not finished on (2) yet. Try to exhibit an isomorphism, e.g.

All right. Do you remember how to divide complex numbers? The same trick can be applied here to find the inverses in \mathbb{Q}[\sqrt2] . Just note that a^2 - 2b^2 \neq 0 whenever a, b \in \mathbb{Q} unless a = b = 0.

Start from the definition of a Cauchy sequence. It usually starts "For all epsilon greater than zero, [...]" Can you choose an epsilon that gives your conclusion?

It looks like you have a mistake in the definitions... What is the definition of Q[sqrt(2)]?

What are the possible amounts of water the distributor has?

All we know about T is that it's a linear transformation. T = 0 is a linear transformation, and it's about as far from being 1-1 as you can get...

I don't know most of the methods you used in your solution attempt, however... Rewrite h(x) in terms of Y = A^tX

There's a 1 on the left side of the integrand, and a 1/2 coming from the fraction on the right. 1 + 1/2 = 3/2...

I still say (expanding a little on my hint) to start with an expression for ∑ xn and try to derive an expression for your series.

No, for reflexive, you'd need to look at a general triple (u,v,w). What does it mean to have (u,v,w) ~ (u,v,w) ? Write it out and find a value for k. You'll need to work with general triples for all of the axioms for an equivalence relation. (if you really get stuck, you might work with...

It's somewhat hard to start from your f(x) and find a series you know. Instead, try starting from a series you know and apply these methods to get f(x).

No. You want to show that every element of A is an element of B. All you showed is that neither contains an even integer. Try writing 7 + 8a in a form that shows it is in B.

Just simplify 1/(2n)²

It looks like we're missing some information. Were there additional conditions given? (e.g. y(0) = ? and y'(0) = ?) Also, what did the DE look like after you applied the Laplace transform?

Well, what are the basic open sets in the discrete topology? Which of these are open in the topology generated by S and which aren't? (by the way, the topology generated by S is far from the standard topology)