Recent content by hmmmmm

I like using boxes in my notes, but I always go for my notes being nice and clean and clear so I don't use any colour or fancy rendering as it distracts me, that's just personal opinion though.

That's an entirely different situation, I like Serena is simply saying that if we have associativity and $a(bc)=(ab)c$ then we may simply write $abc$ in this situation as the parenthesis are irrelevant.

Not having applied for a Phd yet I cannot give you that great advice but I may well be applying for one after my masters and did think about applying for one this year so I have a little bit of experience. I'm not sure how much you have looked into this but when you are applying for a Phd you...

Re: axiomatic approach 2 $\frac{ad}{bd}=ad.\frac{1}{bd}$ by the definition the using the inverse axiom $=ad.\frac{1}{d}\frac{1}{b}=\frac{a}{b}$ hence result

Re: axiomatic approach 2 Oh right I read it as (and I just assume that it is supposed to be) $a+b=b+a$. I suppose that could still be an axiom, just says everything is equal though.

Re: axiomatic approach 2 What do you mean that axiom 1 is "wrong"? Unless I have made a mistake I would have: $\frac{(ad+bc)}{bd}=(ad+bc).\frac{1}{bd}$ by the definition. $(ad+bc).\frac{1}{bd}=\frac{1}{bd}(ad+bc)$ by axiom 3. $\frac{1}{bd}(ad+bc)=\frac{1}{bd}ad+\frac{1}{bd}bc$ by axiom 5...

Re: analysis suggetion A pretty standard introduction to analysis textbook is the principle of mathematical analysis by Rudin. However I would say that this is pretty dense if you have not done any analysis before. I remember I tried to do some advanced reading for my first course in analysis...

Re: Simple question on polynomial ringsWhen we write F[x_1, x_2, ... ... , x_n] where F It does stand for a number of different structures in the same way that $R$ stands for different structures but that is because the $F$ can represent different fields. So for example the polynomial ring...

If I have the following operator for $H=L^2(0,1)$:$$Tf(s)=\int_0^1 (5s^2t^2+2)(f(t))dt$$ and I wish to calculate $||T||$, how do I go about doing this: I know that in $L^2(0,1)$ we have that relation:$$||T||\leq \left ( \int_0^1\int_0^1 |(5s^2t^2+2)|^2dtds\right )...

Could you not just write "this need explanation" or why "why is this clear" or even just say to them thatyou can't write "this is obviou" you need to explain why it is obvious (i.e. give a proof) I don't think it's too hard to do that and not be rude, you hardly need to walk up to them as say...

I'm not sure I'm allowed to pitch in twice (especially when I'm just making suggestions of things I like as opposed to my "favorite things" but oh well...) I have just been doing a little bit of reading for my final year dissertation which very roughly is on foundations of mathematics and was...

I think that (one of) my favorite things is Sylow theory/ nilpotent groups. More specifically showing that nilpotent groups are the largest set of groups which behave as abelian groups do with respect to Sylow theory. I think the fact that I'm finishing my undergraduate studies and remember in...

A transitive set is one in which all elements are subsets, now for 1. you have that the only new member that you have introduced is $A$ and it is a subset so the set is transtitve. Imagine the tansitive set to be $A=\{1,2,3,4,5\}$ where these are defined in the usual way (in terms of the empty...

If you consider the naturals (any subset) or rationals or something with the discrete metric then these are open, so you have (at least) countably many countable sets that are open :)

I'm not too sure how to mark a thread as solved or something but my confusion here came from thinking that unions and power sets preserved well ordering, which they do not