@JasperLoy It is, I took a gamble because I didn't understand one concept out of all the topics so I hoped it wouldn't be on the exam but there was 20 points worth of those topics on it lol
A parity of an integer, by definition, is on which equivalence class mod 2 it belongs. 0 belongs to [0] in Z/2Z as 0 is divisible by 2, hence it's obviously even.
@robjohn I just asked on a certain network this question and I receive only wrong answers. It looks like that most of them say it's neither even, nor odd.
Yes, I prefer option number 2. Texas is a terrible place to work. Salaries are low, and employer benefits are well below national averages. Laws are pretty staunchy skewed against employees in favor of employers, as well.
There was this "credit bubble", for a while, credit was too easy to obtain, based on the premise the economy would continue to improve. The first decade of this century showed that optimism was unfounded. Mass foreclosures ensued, a lot of banks needed to be bailed out, due to unwise mortgage investments.
Loans aren't necessarily bad-suppose you own a trucking company, and can double your earnings with another truck. If the cost of the loan on top of your other expenses is still less than double your current costs, it makes sense to borrow the money.
@TedShifrin, et al. - I am looking for a quote which I believe was attributed to Riemann that went something like, "The difficulty is not in the proofs, but knowing first what to prove."
@DavidWheeler: Usually, over here loans are taken out for acquiring flats or houses. I think the banks require one to at least have a fortune of 30% of the loan they want to acquire.
@DavidWheeler: But for most people it is never paid back. Just the interests. So the house/flat basically belongs to the bank.
I'm not sure about now...for a while Fannie Mae was floating loans with 10-15% down. The lower down payment was typically made attractive to lenders by rolling in PMI (default insurance).
I often hear questions like "Why do you attend such problems, calculations?" or "Who cares about them?" or "What are they good for?". Now, more than ever, I'm sick and tired of these questions.
"not everyone agrees that manifolds should be second countable" is technically true but nonetheless misleading; anybody working on locally euclidean spaces that aren't second countable is far from the mainstream
and his theorem of Whitney assumes second countability
indeed every $n$-dimensional topological manifold can be embedded into $\Bbb R^{2n}$; this is recent, not due to Whitney (who did the smooth case). Whitney's proof works for topological manifolds to show that they embed into some big $\Bbb R^N$; his reduction of $N$ to $2n$ (or even $2n+1$) is not valid in the topological category
@teadawg1337 But I haven't really learn that yet, indeed. I wonder if we cannot get the canonic way of the polynomial and then get the coordonates of the maxinum ?
@robjohn I know it's between 6.48 and 6.52, but I can't manage to prove what the exact value is...
There is something I don't understand, a group action on a set A means g in G acts as a permutation on A in a manner consistent with group operations in G.
Let $x(t)$ be the sign with Fourier transformation
$$X(\omega)=\delta(\omega)+ \delta(\omega-\pi)+\delta(\omega-5)$$
and let $h(t)=u(t)-u(t-2)$.
Is $x(t)$ periodic?
Is the convolution of $x(t)$ with $ h(t)$ a periodic sign?
Can convolution of two non-periodic signs be a periodic sign?
How ...
We also require that $e\cdot a = a$, that is, the identity of $G$ induces the identity permutation. It's very similar to how the group of multiplicative units (of a field) acts on a vector space.
It also tells you the algebraic multiplicity of an eigenvalue, which bounds its geometric multiplicity (is an upper limit for the dimension of an eigenspace). Minimal polynomial gives no information about that.
@Alessandro Hallo!!! Ja, ich bin noch wach.. Ich habe im Moment viele Aufgaben auf. Bis am Donnerstag muss ich in 2 Fächer Aufgaben abgeben.. Was gibt es neues bei dir? :)
Let $x(t)$ be the sign with Fourier transformation
$$X(\omega)=\delta(\omega)+ \delta(\omega-\pi)+\delta(\omega-5)$$
and let $h(t)=u(t)-u(t-2)$.
Is $x(t)$ periodic?
Is the convolution of $x(t)$ with $ h(t)$ a periodic sign?
Can convolution of two non-periodic signs be a periodic sign?
How ...
