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May
19
revised Short exact sequence - Why doesn't this argument work?
tidy up mathjax
May
14
comment Proving a trigonometric identity: $\frac{\cos x}{1-\sin x} -\tan x = \sec x$
@User58220: Why on earth not? The only issue to watch out for with cross-multiplication is that it can introduce extraneous solutions where either (or both) of the denominators is zero. But that has nothing specifically to do with trig.
May
10
comment In how many ways can a $5 \times 5$ matrix be formed such that sum of row elements and column elements are $4$ and entries are $0$ or $1$?
No, explaining how you got the number 120 is the answer. ;-) But yes, the number of 5 × 5 matrices satisfying these conditions is 5 × 4 × 3 × 2 × 1 = 5! = 120.
May
10
comment In how many ways can a $5 \times 5$ matrix be formed such that sum of row elements and column elements are $4$ and entries are $0$ or $1$?
OK, I edited in some more explicit hints.
May
10
revised In how many ways can a $5 \times 5$ matrix be formed such that sum of row elements and column elements are $4$ and entries are $0$ or $1$?
added 503 characters in body
May
10
answered In how many ways can a $5 \times 5$ matrix be formed such that sum of row elements and column elements are $4$ and entries are $0$ or $1$?
May
5
comment I thought the | symbol meant “divides by”, but in set theory, does it mean something different?
Another place where $|$ is commonly used with a different meaning is in probability theory, where ${\rm P}(A \mid B)$ denotes the conditional probability of event $A$, given $B$.
Apr
29
comment What is an Empty set?
Since you've taken the existence of (an) empty set as an axiom above, it might also be worth pointing out that there's nothing fundamentally unprovable about it; i.e. that, in set theories including some form of specification, the existence of an empty set follows straightforwardly from the existence of any set.
Apr
29
comment In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse. Why?
@msouth: If the triangle growls at you when you approach it, it's probably not friendly and you should not try to pet it.
Apr
26
revised Probability of a pair of red and a pair of white socks among five chosen
the original version had a / before the last binomial
Apr
26
comment Probability of a pair of red and a pair of white socks among five chosen
Why did you choose that particular set of binomial coefficients as your solution? I assume you had some reasoning behind it, and didn't just pick random numbers out of a hat (or a box). If so, please explain that reasoning.
Apr
25
comment Understanding the trivial primality test
... In practice, I believe most efficient primality tests typically start with trial division by a precompiled list of small primes, and then (if the number passes the trial division test, and is larger than the square of the largest divisor tested) switch to more advanced algorithms like Miller-Rabin‌​.
Apr
25
comment Understanding the trivial primality test
However, if you're only interested in the primality of a single number $n$, it generally takes more effort to find all the primes up to $\sqrt n$ than to simply try all possible divisors, prime or not, up to $\sqrt n$. That said, one can easily optimize the example code to skip some obviously non-prime numbers (such as all multiples of 2, for a trivial x2 speed-up). And of course, if you want to do a lot of primality tests for similar-sized numbers, pre-compiling the list of possible prime divisors becomes more attractive.
Apr
25
revised Understanding the trivial primality test
use <pre> markup to highlight the loop condition; consistently use lowercase n for the candidate prime
Apr
25
comment Understanding the trivial primality test
I've edited your question to also include the loop body (or what I assume it must look like, anyway), since it seems relevant to the question. Please check that it approximately matches what your book has, and if not, correct it. Thanks!
Apr
25
revised Understanding the trivial primality test
added missing loop body, plus link to page explaining the syntax
Apr
24
comment Am I misinterpreting this matrix determinant property?
@Mahesha999: It's just saying that if you multiply one row or column of a matrix by a constant $k$, the determinant of the resulting matrix will be $k$ times that of the original.
Apr
22
comment Inequality with (1-x) as denominator
@ruakh: It's pretty trivial to see that the LHS of the original inequality is undefined iff $x-1=0 \iff (x-1)^2 = 0$.
Apr
19
awarded  Taxonomist
Apr
16
revised Caden has 4/3 kg of sand which fills 2/3 ​​ of his bucket. How many buckets will 1kg sand fill?
typo