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 Yearling
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Jun
5
comment What Constitutes a Pattern
@Prometheus But all of mathematics can be viewed as a sequence of integers via Godel numbering. It may seem to take the aesthetic beauty away. So consider the sort of "ultimate pattern" of all true statements of some logic, turned into integers via Godel numbering and put in ascending order. Quadratic reciprocity is somewhere in there, as an entry. But I do see your point. This is obviously a poorly defined (and possibly impossible to resolve) thought of mine.
Jun
5
comment What Constitutes a Pattern
@Jared Exactly. So with this definition of sequence, given any finite number of terms there exist countably many sequences which can be "extensions" of this finite tail.
Jun
5
answered Algebraic Closure terminology doubt
Jun
5
asked What Constitutes a Pattern
Dec
30
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.
Nov
28
awarded  Yearling
Oct
8
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.
Oct
8
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
Oct
8
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.
Oct
8
comment How to combine OR linear inequality with absolute value
Try doing some examples -- which $x$ satisfy $|x-2| < 1$?
Oct
8
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).
Oct
7
comment Suppose that the sequence ${a_n}$ is monotone. Prove that it converges iff ${a_n^2}$ converges.
@frank000 duly noted, thanks
Sep
30
awarded  Explainer
Sep
28
answered How do you define Dimensions in general?
Sep
26
comment What does $p_j(x)$ mean?
@andre Yes, oops
Sep
25
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 $D$.
Sep
25
comment What does $p_j(x)$ mean?
The binomial symbol is used in $\LaTeX$ by writing \binom{n}{k}.
Sep
25
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.
Sep
25
comment Exponential Functions Proof
To get $5^{x+h}$ replace your parentheses with curly braces {}.
Sep
25
revised For any two Ideals $A$ and $B$,$A+B=\langle A \cup B \rangle$
deleted 5 characters in body