Hi all, thanks for your replies. I agree that taking the set [a,b] x [c,d] as contained in a larger open region is the most sensible interpretation. I have seen it implied, however, from what I would think are 'respectable sources' that this isn't necessarily the case. I wonder then if it's just...
Something has been bugging as of late: usually, derivatives (ordinary and partial) are defined for interior points. However, I often come across statements in which they seem to also be defined for boundary points. For example, Leibniz' rule of integration, as usually stated, assumes some...
Ok so I'm tutoring for a class this term which is supposed to be an intro to mathematical proofs. One kid asked me how to understand sentences like "Let x and y be real numbers then x = y or x =/= y.". I'm over simplifying, between - it's the use of anonymous variables that seems to bug them. I...
Here's my situation: I'm a math student in their second term of their junior year. I didn't do so good in my first 2 years of college, and even failed a couple of classes (I did manage some good grades here and there though). This was mostly due to a poor work ethic and perhaps some other things...
Where n >= 2.
Is this true or false? I only got so far:
If K is a subgroup of index 2, then it's normal. K is normal in Sn, so it's a union of conjugacy classes. Also, since |An K| = |An| |K| / |An intersection K| = 1/2n! * 1/2n! / |An intersection K| <= n!, then 1/4n! <= |An intersection...
Homework Statement
Find all the normal subgroups of S3xS3
Homework Equations
The Attempt at a Solution
I know that whenever N1 and N2 are are normal subgroups in S3, then N1xN2 is normal in S3xS3. The problem is that there might be normal subgroups in S3xS3 than those obtained...