Recent content by scinoob

Okay, that clarifies it, thanks guys! Sorry, I'm not very experienced in these types of more rigorous approaches to math yet and sometimes fail to see/remember certain parts of definitions which turn out to be crucial.

I am trying to understand the definition of compact sets (as given by Rudin) and am having a hard time with one issue. If a finite collection of open sets "covers" a set, then the set is said to be compact. The set of all reals is not compact. But we have for example: C1 = (-∞, 0) C2 = (0, +∞)...

Hi everybody, I apologize if this question is too basic but I did 1 hour of solid Google searching and couldn't find an answer and I'm stuck. I'm reading Bishop's Pattern Recognition and Machine Learning and in the second chapter he introduces partitioned vectors. Say, if X is a D-dimensional...

I am not sure. Do you mean that the sample space is the set of all sets for which set operations (like union, subtraction, etc.) can be performed? If so, could you give an example of sets for which these operations are inadmissible?

Oh, it's from your post (second sentence) :)

Thanks micromass, I wasn't aware there were two different meanings of the term 'complement'. One last thing on this, could you tell me what is meant by 'the state for all set operations'?

I am reading Introduction to Set Theory (Jech & Hrbacek) and in one of the exercises we're asked to prove that the complement of a set is not a set. I get that if it were a set that would imply that "a set of all sets" (the union of the set and its complement, by the axiom of pairing) exists and...

I think the notation for probabilities and conditional probabilities is not the same and therefore there is no typo.

[PLAIN]http://www.inference.phy.cam.ac.uk/itila/http://www.inference.phy.cam.ac.uk/itila/ I would say start with MacKay's book on information theory. Pretty good and comprehensive.

Good point. In this case I mean tossing the same coin 10k times. In other words, it's the same coin with some unknown bias θ. The posterior distribution represents the degree of belief in each value for θ.

Hello everybody. This is my first post here and I hope I'm not asking a question that's been addressed already (I did try to use the search function, but couldn't find what I'm looking for). Both the Bayes theorem and the law of large numbers are mathematical theorems derived from...

Yes, I do understand it that much. So I guess it could be more than 5% after all. I think what you're suggesting would be very helpful indeed, I like to visualize things to get a better intuition. Thanks again!

I haven't. I have something like a 5% understanding of Minkowski space, but I am in the process of studying it. I also have a somewhat good intuition about a light cone, but still far from what I want. Thank you for the suggestion!

Thanks a lot guys, really appreciate it. I think I finally understand it now. Does Δx' actually have any meaningful interpretation then? With my updated understanding, I would say it represents the spatial distance between two events which may or may not have happened simultaneously. Is this...

I think you're right, I am overthinking it. But now it's almost clear :) There is one last issue that I think would finally allow me to close the last page of this chapter. The Lorentz transformation equations for length and time (equations 1 and 2 from my original post) seem quite symmetric...