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 Dec30 comment AMC Putnam 1986 № B2 Since everything has positive degree (there are no constants), there is the trivial solution $x = y= z = 0$, but also any solution of the form $x = y= z =$ anything and $a=$ anything else will do. Nov28 awarded Yearling Oct8 comment How to combine OR linear inequality with absolute value My example wasn't intended to be the exact same as your question. Try out some examples, and see if all the inequalities you can think of can be written in that form. Oct8 comment Algebraic topology in high school? Ah, the book is by Hilbert, and available here: amazon.com/Geometry-Imagination-CHEL-Chelsea-Publishing/dp/… and notes by Rob Kusner are available here: gang.umass.edu/~kusner/class/462hw Oct8 comment Algebraic topology in high school? This seems really interesting to do. The only thing is that I'm not sure how one would present algebraic objects to high school students and have time to do interesting topology. I've heard of a book (haven't read it) called "Geometry and the Imagination". A professor at my undergrad taught a course with the same title, so I'll look for any notes on that and let you know if I find any. Oct8 comment How to combine OR linear inequality with absolute value Try doing some examples -- which $x$ satisfy $|x-2| < 1$? Oct8 comment How to combine OR linear inequality with absolute value The way I think about this is that $x$ is at most ___ away from the midpoint of $-10$ and $15$ (remember that absolute value tells distance). Oct7 comment Suppose that the sequence ${a_n}$ is monotone. Prove that it converges iff ${a_n^2}$ converges. @frank000 duly noted, thanks Sep30 awarded Explainer Sep28 answered How do you define Dimensions in general? Sep26 comment What does $p_j(x)$ mean? @andre Yes, oops Sep25 comment What does $p_j(x)$ mean? So essentially the author is choosing a specific basis for the vector space of all polynomials in $M$ variables of degree less than or equal to $D$. Sep25 comment What does $p_j(x)$ mean? The binomial symbol is used in $\LaTeX$ by writing \binom{n}{k}. Sep25 comment What does $p_j(x)$ mean? It looks like $\binom{M+D}{M}$ is the number of monomials of degree less than or equal to $D$ in $M$ variables. So $J$ would then be an enumeration of them. EDIT: I misunderstood what your question was asking. That symbol is the binomial symbol, and you can find information (now that you know its name) on Wikipedia. Sep25 comment Exponential Functions Proof To get $5^{x+h}$ replace your parentheses with curly braces {}. Sep25 revised For any two Ideals $A$ and $B$,$A+B=\langle A \cup B \rangle$ deleted 5 characters in body Sep24 comment For any two Ideals $A$ and $B$,$A+B=\langle A \cup B \rangle$ @spectraa An "additive subgroup" is just a subset $S \subseteq X$ that is closed under addition -- $a + b \in S$ whenever $a$ and $b$ are both elements of $S$. As Nimda mentioned, any subring must be an additive subgroup, simply by the definition of ring. So the statement I mentioned can be read as "Whenever $S$ is a subset of $X$ that contains $A$ and $B$, and is closed under addition (in particular $S$ could be a subring of $X$ containing $A$ and $B$), $S$ must contain the ideal $A + B$." Sep23 answered For any two Ideals $A$ and $B$,$A+B=\langle A \cup B \rangle$ Sep23 comment How to construct a smooth curve whose range is dense in $\mathbb R^2$? My first thought is to use the topologist's sine curve in some way. Sep23 answered Summable enumerations of $\Bbb Q$