Can all functions be expressed with the standard mathematical operators and elementary functions? In other words does their exist things that are functions but cannot be expressed using operators $+-*/$ and elementary functions such as powers, trig functions etc.?
@northerner this question only makes sense for functions from (subsets of) the real numbers to the real numbers and the answer is that almost all functions are not of this form
@user2103480 so how do you encode the concept of an order?
and for orders that you can define by formulas, we can reason without resorting to a superset. A simple case is when you have a class $R = \{x \mid \varphi(x) \}$ defined by some formula and then $\psi(x,y)$ defines a total order by just the usual axioms. If $\psi(x,y) \land \psi(y,z)$ then $\psi(x,z)$, for arbitrary $x,y,z$ with $\varphi(x), \varphi(y), \varphi(z)$ etc
But expressing something like "all orders are isomorphic" is best done by just expressing the thing in set theory, else I think we have to go up one level and say that for all formulas that encode an order, there is a bijection between the classes
And in the end this pushes the real problem just one level higher in the hierarchy: the fact that all this is idiocy
@copper.hat lol w/e dude!... try not to lose it its a gem! its a glimpse of the future! do you like kuhnian paradigm shifts? physics revolutions? eg on the level of discovery of the photon? its 12:58 and think youll like it even more than random chat topics+chatter :)
So we assume that ZF is consistent and we prove in ZF that all the structures that satisfy arithmetic and second-order induction (any inductive subset must be the whole set) are isomorphic
so what this means is that for any class/set that "satisfies" the ZF axioms internally, all the natural number structures inside the thing are isomorphic
but across these things which we call models, the naturals can again be wildly different
Accordingly, a coherence law in an (n,n)-category such as a bicategory (n=2) or a tricategory (n=3) or a tetracategory (n=4) is in degree n+1 a complicated equation that asserts that a certain contractible space of higher morphisms is exactly equal to the point.
@copper.hat ok know youre a different generation (like me), but anyone who doesnt watch 1 youtube video a day, possibly on their phone, is now abnormal :P "slogging thru" what? it sounds almost like grading papers... o_O
Why is neural networks being a deterministic mapping not always considered a good thing?
So I'm excluding models like VAEs since those aren't entirely deterministic. I keep thinking about this and my conclusion is that often times neural networks are used to model things in reality, which often t...
Establishing shot. An empty back alley in Paris. It rains. The sound of footsteps, each making a splash, is slowly impeding at an increasing pace. The protagonist enters the screen in a hurried state. He wears a trench coat and a fedora, the only source of light emanating from him is the lit cigarette slowly burning out in the corner of his month. He hastily looks around, mumbles something inaudible (actually, it's just French), then continues hurrying, towards the camera. Suddenly, a lightning strike. Then, a gunshot. Black screen. Silence. The black screen fades and the protagonist falls …
@copper.hat I have solved the problem..But tell me something...How to stay motivated that the events are independent of each other pkease explain this to me.
I think it's a reasonable assumption, @user586228, although it may not be. After all, if I'm terrible at math, I will probably be terrible at physics, too. But this is multiple choice. You have to pick the best answer, and it's the only reasonable answer.
@user586228 it is an assumption that i made. you would need to check with your instructor.
@vzn slogging... i can't tell you otherwise i would have to kill myself.
@user586228 i don't know what the context of source of the problems are, but generally there are some implicit assumptions that can be made. again, ask your teacher.
@NoName But Spivak assumes no prior knowledge of calculus whatsoever. An analysis course would assume that and also wouldn't teach the concrete and more applied things.
You don't need to have done computational calculus exercises (like volumes of solids), but you need experience with calculus. But I'm running off to dinner now.
Actually, @copper, I think Calculus on Manifolds is his worst book. I think you have to know the subject (and certainly know multivariable calculus) before attempting that book. I much prefer my own. (Duh.)
@TedShifrin i agree, but it needed to be light :-). my analysis was good back then, i was interested in forms, etc. i always found the notion of formal sums a little entertaining until i hit tensor products.
@EdwardEvans it would be classed as software development, but it is a bit more complex. i am familiar with both design flows, eda tools and am broadly trusted in the south bay.
I am wondering whether or not this is the right sketch of the derivative in the picture below:
UPDATE:
Here is the function as it appears in the question (please disregard the pencil marks):
@EdwardEvans a few things to keep in mind. 1. its never about the software. 2. its about keeping your customer happy. 3. if the software looks good you have wasted time.
alas feel scrum is not so agile with too much emphasis on estimation, @#%& at least thats how it played out near me o_O in the sense of "exploding grenade" being "near" o_O
:D Okay, I guess if I get the job I'll experience it for myself. The good thing is that the position has a good "intro program" and the company has very good reviews as an employer
@vzn I'm in my master's at the moment but I'm not doing well enough to justify continuing. I've been trying to force it for 1,5 years and my mental health is just divebombing so I need to get out to retain my sanity.
@EdwardEvans i don't know you so this is prob not good advice. it is a good idea to get a broad idea of how everything fits together at a company, not just focus on one silo.
@EdwardEvans sales people work to the maxim ABC = always be closing. while not directly applicable ti research, it is a good reminder to decide the course and follow it out.
I need to do something other than study at the moment and I'm looking to develop new skills elsewhere. Programming at university was fun and I always had an interest in it, so I guess I'll dive into it at a company that seems to have a nice atmosphere and a nice working culture. After I get some experience I can always move around.
I am wondering whether or not this is the right sketch of the derivative in the picture below:
UPDATE:
Here is the function as it appears in the question (please disregard the pencil marks):
