60,110 reputation
568159
bio website thomasoandrews.com
location Cambridge, MA
age 49
visits member for 3 years, 11 months
seen 10 hours ago

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


11h
comment Given automatic equation solvers exist, should one know how to solve equations by hand?
Depends on whether you want to understand stuff, or just get a solution. Learning to understand stuff is far more important than any other part of learning.
11h
comment Bachmann's construction of the real numbers
The book probably references Bolzano for what is now called the Bolzano-Weierstrass Theorem. Bolzano seems a bit early to have defined the real numbers this way, but he proved the reals had the property.
12h
comment Do every math operation derive from sum?
I can't follow any of that, @BrunoCosta, but I'm pretty sure that is not what I'm saying. I'm saying the above definition of $a\cdot b$ using repeated addition doesn't work except for $b$ a positive integer.
12h
comment Do every math operation derive from sum?
@BrunoCosta Doesn't work for $b$ not a positive integer, however. What does it mean to add something to itself $-2$ times or $1/2$ times, or $\sqrt{2}$ times?
12h
comment Do every math operation derive from sum?
I have no idea what your question means, so I'd probably not be able to help.
12h
comment Do every math operation derive from sum?
It's not really a rigorous statement, so it doesn't really have a proof.
15h
comment (Concrete) mathematical aspects of programming
Multidimensional arrays are not matrices. They look the same, but they are semantically different. A matrix can be respresented as an array, but not all arrays are matrices.
15h
comment $d(n)$ is odd iff $n = k^2$
Ah, a commenter is not an answerer. And the whole point of marking questions as duplicates is to avoid adding the same answers over and over again to repeated questions. I've seen this particular question asked here several times recently.
15h
comment $d(n)$ is odd iff $n = k^2$
It's unclear if you are quibbling whether the question is a duplicate, or you are asking me to answer this duplicate question.
15h
comment $d(n)$ is odd iff $n = k^2$
Um, what? @Megan The quest is exactly the same. "A number is a perfect square" iff $n=k^2$ for some integer $k$.
17h
comment Why is $\mathrm{arctan}(0)$ not infinity?
Sure, but is also could have been confusion about the term "inverse function." It might well have been a $\tan^{-1}$ problem, just saying, you are supposing that, when it could have been other confusion.
18h
comment Why is $\mathrm{arctan}(0)$ not infinity?
But, of course, this question never mentions the notation $\tan^{-1}x$.
18h
comment Parametrization of solutions of diophantine equation $x^2 + y^2 = z^2 + w^2$
Your English is very rusty, to the point of being useless. "I led the equation" doesn't make sense. "And will solve the equations as 1000 years ago?" reads like a question, but it is unclear what the question is. Try to be as direct as possible, don't be obtuse, because your English is, unfortunately, obtuse already. @individ
18h
comment Parametrization of solutions of diophantine equation $x^2 + y^2 = z^2 + w^2$
What are you talking about, @individ. What odds? And what do you mean about 1000 years ago?
18h
comment Parametrization of solutions of diophantine equation $x^2 + y^2 = z^2 + w^2$
That certainly, is at heart, the source of all the cases, @user170039, by unique factorization on $\mathbb Z[i]$.
18h
comment Parametrization of solutions of diophantine equation $x^2 + y^2 = z^2 + w^2$
Well, that wasn't part of the question, but the same approach works as long as you can find one solution. The trick was to start from a particular rational solution to $ax_1^2+by_1^2-cz^2=j$. Then any rational-sloped line through that solution has (at most) one other solution, and that solution will also be rational. This finds all rational solutions. But you need to find one solution, first. @individ
18h
revised Parametrization of solutions of diophantine equation $x^2 + y^2 = z^2 + w^2$
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22h
revised Parametrization of solutions of diophantine equation $x^2 + y^2 = z^2 + w^2$
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23h
revised Parametrization of solutions of diophantine equation $x^2 + y^2 = z^2 + w^2$
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23h
answered Parametrization of solutions of diophantine equation $x^2 + y^2 = z^2 + w^2$