Why is any left coset of a subgroup H equal to a right coset of some subgroup not necessarily H?

Is there a generalization of the concept of the conjugate in algebraic sets that are divided into pairwise disjoint subsets? Is this only a result of the need for an inverse to the exponentiation operator, and the fact that its properties lead us astray (into the irrationals and the imaginaries)? Are there other conjugates than a radical conjugate ( Read more... )

My young student calls me "the coolest math geek (she's) ever met."

I don't know if I'm a math geek yet, but it's nice to be cool.

He asks: Consider the set Q = Z X Z - {0}. Define a relation R on Q by ((a,b),(c,d)) is in R if there exists an integer k, such that ad = bc = k.

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Well, it's sort of like the rational numbers. But is there actually a question here, or did he simply forget to type the question part?

Related, I think, to the powerset question I asked the other day:

If a number is the product of n unique primes, it has 2n factors?

Here's my current physics problem. I already know the answer to part B because I gave up:( cut for image )

Another way to understand the cylindrical shell formula is as the derivative of the volume of a cylinder with respect to its radius, or the instantaneous rate of increase of the volume of a cylinder per increase of radius. If the height depends on the radius, as in most cylindrical shell problems, then this height is simply multiplied by the ( Read more... )

It's easy to be impressed by what one doesn't understand very well.

--- G. H. Hardy

There are many faces to the mask of uncertainty.

--- Richard Bellman

The artist is nothing without gift, but the gift is nothing without work.

---Émile Zola

Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them ( Read more... )