Recent content by icantadd

I have been exploring an algebraic structure with a map (_)* such that (x)*** = (x)* but in general it is not an involution. Also, the set of elements e such that e** = e do not form a substructure because they are not closed to addition. Has anyone seen such maps before, or know/can...

Thank you for the reply!

I have a general sort of structural question. I have been reading a lot of maths papers lately, and it seems there are some isomorphisms that people omit from their calculations. For example, in a category with a terminal object, 1, A \cong A \times 1 where the isomorphism is given from left...

Let R be a commutative semiring. That is a triple (R,+,.) such that (R,+) is a commutative monoid and (R,.) is a commutative semigroup. Let {\mathbf \alpha}_i = \alpha_1,\alpha_2,\ldots,\alpha_n . The n-variate indeterminate is just free monoid on n letters. However, it is common to...

Definition: A semigroup is a pair (R,op) where R is a set an op is a binary operation that is closed and associative. A commutative semigroup is a semigroup where op satisfies for all a,b in R, op(a,b) = op(b,a). A monoid is a semigroup where with an identity,e, for op, satisfying for all r in...

Yeah, now it looks good. If you need to justify the distances, ue pythagoras theorem.

Okay, I see the pic now. You are starting from the origin. Just calculate where the point is in the table.

Okay, you're fine you have to use the inductive hypothesis combined with a brief observation. You assumed that 6 | (n^3+5n) for all n. So you then consider the case (n+1)^3 + 5(n+1) which you have shown equals (n^3+5n) + (3n^2+3n+6) . Looking at the left terms you can use your inductive...

What is the definition of an index?

Yeah, I was thinking about that... Does taking the gcd of a group with infinite order make sense?

You can get there! Yup, okay, we have k^n = 1. Now what can you tell me, using Lagrange about n and |K|? Write that down. Now if you assume k is also in H, what does that imply?

No, 1 is in H and K because H and K are subgroups of G. Are you sure you can assume finiteness here? Here is a different way to approach. Pick an arbitrary element,k, in K. Now state something about the order of k. Now what happens if you assume k is in H? What is true about all the...

Here is a sort of idea I have for counting polynomials. Let's generalize the problem a bit. Suppose we have n variables. One can think of the set of elementary symmetric polynomials in n variables as the power set of the n element set and factoring out by size. Then pick any partition...

Typically an element is either in a set or not. Are you talking about a "fuzzy" membership function?