Recent content by The Chaz

Just a note on (iii): $R_1 = -2(R_3) - (R_2)$ So the rows are linearly dependent.

Purity.

Agreed!

Sorry for the necroposting... 1.b.i "Point-slope form": $$y-y_1 = m(x-x_1)$$ I recommend this when they say "find **an** equation...", as there are infinitely many such equations (and some are easier to find than others!) So $$y - 3 = \dfrac{-7}{3} (x - (-1))$$, or $$ y -3= \dfrac{-7}{3} (x...

I don't follow. We have $5|2+3$, yet five divides neither of the summands. Are you referencing a certain property of this ring?

Doh! I'll have to fix it the next time I'm at a proper computer :)

Certainly, adding half the square of HALF the linear coefficient is the result, but I would take a slightly different approach... We start with squaring binomials of the form $(x + d)$ for integers $d$. I prefer to skip $d = 1,2$, as they don't necessarily lend themselves to an educated guess...

Then taking (natural) logs on both sides, we find that

On a related note, which software do you (all) suggest for a Mac user? I had downloaded "Texit" (or something like that)... it was a 2gig file that I could never get working. I would love to be able to communicate math via LaTex in .pdf files, so any suggestions along those lines would be...

So LaTex in brackets is centered? Not sure I get the syntax, though I'm trying to scroll through it on the mobile...

I came across a riddle (surely with some number-theoretic background). Paraphrased: A solution would be nice, but I'd also be interested in knowing the origin and/or common name (phrasing) of this puzzle. Thanks.

Here are a few: http://codecogs.com/latex/eqneditor.php (WYSIWYG) http://tobi.oetiker.ch/lshort/lshort.pdf (PDF) ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf (FTP)

Let f(x) = |x|/x a. What is the limit of f, as x approaches 0 from the right? b. What is the limit of f, as x approaches 0 from the left? c. Hence, what is the limit of f, as x approaches 0? ------------------------------ The best way to evaluate limits involving absolute values is to use...

Does anyone recommend a particular free (digital) resource on Clifford Algebras? Besides the usual (wiki, wolfram, etc), if possible :D

I know you're new around here ;) , so you might not know that it is preferable to show work. (That might be in the rules...) So I'll get the ball rolling. Letting a , b, c be the (equal) sides of the "big" triangle and A, B, C the angles formed by... oh dear, I have confused the letters. If...