13,937 reputation
11936
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years
seen 7 hours ago

Aged mathematician


6h
comment Generators of elliptic curves?
What do you know, and what have you tried?
6h
comment Does the definition of derivative exclude the possibility for discontinuous rate of change?
It looks to me as if the question is whether, if $f$ is a differentiable function, the derivative $f\,'$ also has to be continuous.
13h
comment How can I find the radius of a circle from a chord and a section of the radius?
It’s standard stuff to find the center from three points $(P,Q,R)$ on the circumference. The perpendicular bisectors of $PQ$ and $PR$ meet at the center. You could turn turn that into an algebraic treatment, I suppose. This can not be the easiest method, I’m sure.
1d
comment Are there mathematical contexts where “finite” implicitly means “nonzero?”
But, you know, in deference to physicists, it’s just as hard to measure a tiny number accurately as it is to measure its reciprocal. I think that in the real world, the logarithmic view makes perfectly good sense.
2d
comment Can you cancel out a term if equal to zero?
In agreement with @cpast, let me say that my rule was for equations only; the corresponding rule for fractions is that you can multiply top and bottom by any nonzero quantity and preserve the value of the fraction (for the cognoscenti, I amplify that I’m speaking of fractions over an integral domain).
2d
comment Find the minimum number of terms in the series it would take before the error would be guaranteed to be less than 10^-9
Are you trying to evaluate the logarithm at a particular number between $0$ and $2$? Or are you being asked this question no matter what number you’re finding the logarithm of?
Oct
20
comment how do I prove that $\mathbb{Q} [x]/\langle x^2 – 2 \rangle$ is a field
This is teh kind of answer I would have given.
Oct
20
comment How does one find/list equivalence classes?
Well, that’s if you need to name them. Ordinarily, that’s not necessary.
Oct
19
comment How does one find/list equivalence classes?
I think if you count the number of classes (and I agree with your enumeration now), you’ll get a clue of how to describe them.
Oct
19
comment How does one find/list equivalence classes?
What do you mean by “find”? Do you mean just to describe them, or to count the number of things in each class, or what?
Oct
18
comment If $a\pmod 3 \equiv 1$ and $b\pmod 3 \equiv 2$, then $ab \pmod 3 \equiv 2$
To be pedantic, I point out that the original (and for mathematicians, right) way to write these relations is “$a\equiv b\pmod3$”. What’s going on is that $\equiv$ is a verb, and “modulo $3$” is an adverb modifying that verb. In Gauss’s Latin, “modulo $3$” means “with respect to the modulus $3$”.
Oct
18
comment line segment intersection strange results
Right. Here’s a case where it’s more reliable to write down the two equations (point-point formula, for instance, for each) and solve the pair of simultaneous equations that you get.
Oct
17
comment $\displaystyle\int \dfrac{\cos(x)+\sin(2x)}{\sin(x)}\text{ d}x$
Oh, sorry, I’m too old. I thought that the integral of tangent was well known, so cotangent (sort of) follows.
Oct
17
comment How do you solve this fraction?
“cross multiplication” is a technique that makes sense only when you have an equation, which you don’t.
Oct
17
comment $\displaystyle\int \dfrac{\cos(x)+\sin(2x)}{\sin(x)}\text{ d}x$
You don’t even need a substitution: after using the double-angle formula, separate the integrand into two fractions, each easily integrated.
Oct
16
comment How can we show that it is an integer 5-adic number?
I prefer the completely simple-minded method I showed you in my answer to your other question, about $1/2$. It’s good for finding the quotient of any two $p$-adic numbers, not just integers.
Oct
16
comment What does the inequality stand?
This is a good example, but I wish you had written a few more words.
Oct
15
comment how find all the zeroes of the polynomial
In your try, you told no lies, but the form you got was not helpful to you, because you didn’t find the zeroes. You need a factorization that looks like $2x(x-r_1)(x-r_2)\dots$.
Oct
13
comment Changing digits of an irrational allowed?
In mathematics, we don’t “allow”. Rather, we insist that any statement you make should be true. Notice that if you change all the $4$’s in $\pi$ to sixes, you haven’t told a lie, because you haven’t made a statement. That is, there has been no equals sign or any other verb. So anybody may make that change in $\pi$, but then it’s up to that person to try to say something true about the resulting number. Like: “it’s no longer normal”. That’s a true statement about your new number.
Oct
12
comment Linear independence and grammar
On the contrary, I think that this distinction is important to keep in the back of one’s mind, sometimes even in the forefront.