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Jun
26
answered Logic question for a program I'm designing
Jun
26
comment Logic question for a program I'm designing
I can't quite understand the problem. So you have a trailer with $10$ slots for boats in it. What does "1C/2K" mean? You can put either one canoe, or two kayaks? You say you need to determine whether or not the trailer is full - what data do you have? Just how many kayaks and canoes are currently reserved?
Jun
26
reviewed No Action Needed Compute the first six terms of the following sequences (start with n = 1):
Jun
26
comment Prove that the characteristic polynomial of a nilpotent matrix is $x^n$
I think that your complaint is that I'm being too rigid, and that we should be able to accept intuitively obvious facts as intuitively obvious without proof. What I'm saying is that if you don't know about factorization, the fact that $x^n$ is the only polynomial whose only root of $0$ isn't intuitively obvious.
Jun
26
comment Prove that the characteristic polynomial of a nilpotent matrix is $x^n$
@Mathmo123 I don't think it's acceptable at all. Maybe $x^5+6x+75x-2x$ has no roots other than the obvious root of $0$. I don't know, it's very hard to tell at a glance. You need the fact that you can split polynomials. You have to at least mention that very non-obvious fact, otherwise what you have doesn't even come close to being a proof.
Jun
25
answered Prove that the characteristic polynomial of a nilpotent matrix is $x^n$
Jun
25
comment Generalization of Liouville's theorem
I think a more natural generalization would be: does there exist a set of functions containing $E$ which is closed under composition, arithmetical operations, and anti-derivation?
Jun
25
comment another counting problem
@user157920 But you are interested in finding a formula, not necessarily a program, right?
Jun
24
comment Factorial of zero is 1. Why?
You could also say there are no ways of arranging $0$ items, because you can't arrange them. A bit like how you could argue that $x/0$ should be $x$, because you're not doing any dividing. For reasons like this, I think edge cases like this are best handled formally, rather than trying to give intuitive explanations, which tend to collapse when examined more closely.
Jun
24
comment Translate a German paper by Hilbert
@amWhy Fair enough. I assumed from your first comment that you were opposed to the question.
Jun
24
comment Translate a German paper by Hilbert
@amWhy "Go for it, then!" Don't be so ridiculous. What's your argument, here, that because one person doesn't have the time or inclination to fulfill a request, therefore that request is too demanding and shouldn't even be posted?
Jun
24
comment Translate a German paper by Hilbert
@amWhy It's five light pages. There's no harm in throwing out a request.
Jun
24
comment Axioms of Euclid
@ArghyaChakraborty The difficulty is that Euclid's axioms are formulated in common english and are therefore vague. The whole problem just isn't precise enough to be given a precise mathematical treatment.
Jun
24
revised Express the area of a circle as a function of $x$
edited tags
Jun
23
comment History of $p$-adic numbers
Thanks! I don't understand that last reference - is "Charlemagne and his Heritage" the name of a book which includes a paper called "The genesis of Hensel's p-adic Numbers"?
Jun
23
asked History of $p$-adic numbers
Jun
22
comment Daily exercises to speed up my mental calculations?
@afedder Only a little bit. You need maybe half your times tables, and being able to recognize $10-n$ at a glance for any $1\leq n\leq 9$.
Jun
22
comment Daily exercises to speed up my mental calculations?
The key to fast mental calculation is numerical fluency, not just practice and having memorized tables and algorithms. I'm competent at mental multiplication because I can visualize grouping objects, and moving along the number line in my head as I do so, not because I know my times tables. So for example, your point (3) is irrelevant. If you are "forgetting" how to do something, that implies you've memorized it without intuitively understanding it, meaning it was useless to you to begin with.
Jun
22
revised Is the set discrete?
edited tags
Jun
21
comment What is that curve that appears when I use $\ln$ on Pascal's triangle?
Roughly speaking, you're looking at the level curves of $\ln({y\choose x})$.