Math Forum / Mathematics / Algebra Help / July 2009

As to my question about the best way to define a k-element subset of members
of J [J = any set of primes] ordered in an arbitrary sequence, should I use
'g_J' throughout, so it's
"Let J be any set of primes.

With thanks to William Elliot for his help on the previous thread.
This is the other property definition I'm working on:
"For any positive integer k and any set C of integers for which (k+1)prod(R)
<= max C, an interval [1, prod(R)] will be said to be _R,C-special_ if, for

Is there any better way to phrase the following:
"For any set K of intervals of length y-x, a variable m([x,y]) will be said
to be K-s-maximal if and only if max {m(I)|: I in K} - m([x,y]) <= s, and
K-r-minimal if and only if m([x,y]) - min {m(I)|: I in K} <= r"?

Trying to get back into the swing of mathematics and realizing how
much I've forgotten is really frustrating. I have been working this
problem and researching for two days now with no luck.
Problem 1:

I'm just wondering about the log.  We all know that:
log(xy)=log(x)+log(y)
log(x/y)=log(x)-log(y)
log(x^y)=y*log(x)

A hopefully quick question:  If x = n^2 + n, what is the value of n
expressed as a function of x?
Thanks in advance to all who respond.

I am still -- I am really embarrassed, and sorry, to say -- perplexed on the
issue of dependency.
I've got a set K(.) that I want to define, which, for one of the
arguments -- ie. 'a' in K(a) -- is  m+(x+y)/2 (m is just a variable). Now, I

Let P(n) be the set of primes not exceeding an integer n.
Let Div(P(n), k) be the set of divisors, in P(n), of an integer k.
I am interested in patterns of integers that share a common set of divisors.
However, the whole presentation of my argument is messed up by the fact that

Let J be any set of primes. For any integer i, let Div(J, i) = {m in J: m |
i}.
'|P A' shall denote 'the set of sets A'.
I'm writing a definition that I've currently put as follows:

I'd like to submit a problem I'm trying to solve, since there're
several days I'm trying to solve without success.
Let Z(N) a finite group containing integer elements from 0 to (2^N) -
1.

Can anyone help simplify?
( A * B * C * D ) + ( A * B * E * C')

I'd like to know the proper way to set up the equation for this math word
problem:
"How many minutes is it before 12 noon if nine minutes ago it was twice as
many minutes past 10 am?"