Recent content by Enzipino

I'm having a bit of problem trying to find isomorphisms between the following groups: $D_6$, $A_4$, $S_3 \times \Bbb{Z}_2$, and $G$. G is a group generated by $a, b, c$ which follow these rules: $a^2=b^2=c^3=id$ (id = identity), $ca=bc$, $cb=abc$, $ab=ba$. I can find isomorphisms between...

In class we had to show that ${A}_{5}$ is cyclic. So what we did was, ${A}_{5}$ is cyclic iff there is an $\alpha\in{A}_{5}$ with $<\alpha> = {A}_{5}$. So, the $ord(\alpha) = |<\alpha>| = |{A}_{5}| = \frac{5!}{2} = 60$. So, $60 = {2}^{2}*3*5$. After this, we said that we could do a 4-cycle...

Oh, I apologize. So then that would be why they did $(6*3)+(3*6)$. I see it now. Well could we have done the numerator in another way? EDIT: OH They have another way to do the numerator which is $(3*3!)+(3*3!)$ which comes out to the same result.

Listing out all the forms of xyz, I have 18. (Kinda seeing where the $6*3$ part is starting to play in).

I believe the xyz part is where I'm getting messed up at. I can see 3 but do I multiply it by 2 because we have two different outcomes? That is we have the first situation being [2|4] and the other in [3|6]? If that's the case then we'd have 6.

I know this should be easy to understand but I just need a little clarification on the last part of my answer for this problem: If three distinct dice are rolled, what is the probability that the highest value is twice the smallest value I started this problem with the understanding that there...

I'm given the following Piecewise function when $f:[0,1]\to[0,1]$: $f(x) = x$ when $x\in\Bbb{Q}$ $f(x) = 1-x$ when $x\notin\Bbb{Q}$ I need to prove that $f$ is continuous only at the point $x=\frac{1}{2}$. For this problem, I know I need to use the fact that a function $f$ is continuous at a...

So I was pulling my hair out at Barnes and Noble doing this problem because I was completely unsure if I could just use Cauchy Sequences to prove this problem since my textbook is mean and likes to not name certain things. I decided to go back and look at some of the previous problems in the...

I was just looking through my textbook to brush up on Cauchy sequences since I was planning on using it for this problem but my book utterly leaves it out. But I did come across this Theorem: Suppose that $$f$$ is a function and $$f:S\to\Bbb{R}$$. If $$f$$ is uniformly continuous on $$S$$ then...

Ah yes, I apologize. It is $\overline{S}$. Thank you very much for the hint! I don't recall covering Cauchy Sequences in my intro class so I will have to read up on it but I do see where I can go with it now.

Hello, I've been attempting to do these problems from my textbook: 1. Suppose that $$f$$ is a continuous function on a bounded set $$S$$. Prove that the following two conditions are equivalent: (a) The function $$f$$ is uniformly continuous on $$S$$. (b) It is possible to extend $$f$$ to a...