57,527 reputation
566153
bio website thomasoandrews.com
location Cambridge, MA
age 49
visits member for 3 years, 9 months
seen 7 mins ago

"Absent-minded" is what they call you when you are a very smart idiot.


19m
comment Proving $\lim_{x\to9}\sqrt x=3$ using Cauchy's definition
It's not $3\epsilon-9<x$, it is $9-3\epsilon<x$. @kuhaku
21m
revised Proving $\lim_{x\to9}\sqrt x=3$ using Cauchy's definition
typp
48m
comment Why does $1+p+p^2+\dotsb+p^{n-1}=\frac{1-p^n}{1-p}$
First of all, I suspect you are misreading your calculus book The value $\frac{1}{1-p}$ only equals the limit as $n\to\infty$. It can't equal the finite sum, since the finite sum obviously differs as $n$ differs...
1h
revised Why does $\lim_{n \to \infty} \sum_{k=1}^n\frac{t^{k+1}}{(k+1)!}=e^t-t-1$?
Parentheses not required here, makes it harder to read
17h
answered Evaluation of an integral of some expressions involving fractions
17h
comment Evaluation of an integral of some expressions involving fractions
Partial fractions is generally not useful with $\sqrt u$ in the denominator, but you can make the expression rational by letting $u=t^2$.
17h
comment Evaluation of an integral of some expressions involving fractions
Do you want $\sqrt{u(a+u)}$ or $(\sqrt u)(a+u)$? Just making sure...
20h
comment Best function getting 0 for odd parameter, 1 for even
I tested it already myself, with a program that computed (-11)%2, GCC on a MacOS X. But I used to test C compilers for a living, so I was pretty sure of the result.
20h
comment Best function getting 0 for odd parameter, 1 for even
Technically, x%2 returns negative values when x is negative, so your first odd is wrong. (I really hate that about C's %.) And no, I didn't downvote. Someone randomly downvoted my answer, too.
20h
comment Best function getting 0 for odd parameter, 1 for even
Yeah, was just noting that it works in general, whatever $f(x)$ is. Although I don't see how this $f(n)$ is particularly "fast." Certainly, faster than computing cosine. But OPs original question is odd, since the definitions at the top are essentially the most efficient ways to implement the functions....
20h
revised Best function getting 0 for odd parameter, 1 for even
added 155 characters in body
20h
answered Best function getting 0 for odd parameter, 1 for even
20h
comment Best function getting 0 for odd parameter, 1 for even
In C or most C-like languages, g(x)=abs(x)%2 is good enough. For $f(x)$, use 1-g(x) or even !g(x)
20h
comment Best function getting 0 for odd parameter, 1 for even
+1 Of course, given any $f(x)$ satisfying this, $g(x)=1-f(x)$ is good for $g$. :)
20h
comment Best function getting 0 for odd parameter, 1 for even
You mean you wanted continuous functions with this property? Because what you defined in the first line were fine function definitions.
21h
comment Why is it possible to find the birth year by subtracting one's age from 114?
@user51189 Probably because of the lack of sentence structure, punctuation, capitalization, or other indications that you are making an effort to write a clear question. And the fact that it is not entirely correct. Just guessing, I didn't downvote, but some people do downvote for those sorts of reasons.
21h
comment Why is it possible to find the birth year by subtracting one's age from 114?
Birthyear+age=year now if, as you say, you've had your birthday this year.
21h
revised Why is it possible to find the birth year by subtracting one's age from 114?
edited tags
21h
comment Why is it possible to find the birth year by subtracting one's age from 114?
If I was born on December 23rd of 1999, that would be wrong, since I would be 14.
23h
revised How do I prove this derivation?
replaced images with mathjax