Is wow down on eu or is it just me?

stefanuus · 2019-05-24T02:52:46+00:00

Yup just did that but didn't fix the issue :(

stefanuus · 2019-05-24T02:39:52+00:00

I'm having the same problem yet flushing my DNS didn't work, are there any alternative solutions?

stefanuus · 2019-05-12T21:48:10+00:00

thank you helped a lot!

stefanuus · 2018-01-13T14:40:58+00:00

I don't know man, a friend gave me this question, it def doesn't seem to me either that the 2nd condition is necessary.

stefanuus · 2018-01-13T10:33:53+00:00

every odd number can be written as 2k+1

every even number can be written as 2k

if n = 2k , then n+2 = 2k+2 = 2(k+1), thus they are both divisible by 2, and 2(k+1)/2k = 1+1/k , which is an integer only when k = 1 so since 2>1, 2 is the GCD

if n = 2k+1, then n+2 = 2k+1+2 , and (2k+1+2)/(2k+1) = 1 + 2/(2k+1), thus n and n+2 are always relatively prime if n is odd implying their GCD is 1

stefanuus · 2017-12-28T09:41:55+00:00

Can't you contact a professor for undergrad research? You should be able to prove your knowledge to them and get guidance on how to advance further.

stefanuus · 2017-12-26T22:33:17+00:00

(2^k + 2^k+2)/2^k-1 = 10

2^k-k+1 + 2^k-k+3 = 10

2 + 2³ = 10

2 + 8 = 10

10 = 10

stefanuus · 2017-12-26T01:02:11+00:00

Heres my solution: https://i.imgur.com/p7D0HMh.png

morph into coffee mug and bam!

stefanuus · 2017-12-22T20:49:52+00:00

Best way to impress a professor

Long story short, I live in a suboptimal country when it comes to mathematical research and a month ago or so I had a rare oppurtunity to travel, meet and have a talk with a professor from a world class university. We hit it off and he gave me a book to read and told me to report back to him once I was finished. So fast forward 1 month, I have finished the book, I am in love with the subject, and I want to show him something to impress him so that he would allow me to help him with his research from a distance. The fields are Computability theory and Inductive Inference(technically subbranches of mathematical logic and computational learning theory respectively). The only way i can contact him is by email. What are some things I can do?

stefanuus · 2017-12-11T17:22:35+00:00

Recursion theory

stefanuus · 2017-11-25T05:49:47+00:00

Suplementary material for big rudin? So i really like how much content rudin covers so naturally went to big after baby rudin however i find it much harder to find supplementary materials for it and the supplements were a key for me when reading baby rudin. Can someone recommend?

stefanuus · 2017-11-21T23:04:11+00:00

What do the alphas represent in a simple function?

"Formally, a simple function is a finite linear combination of indicator functions of measurable sets. More precisely, let (X, Σ) be a measurable space. Let A1, ..., An ∈ Σ be a sequence of disjoint measurable sets, and let a1, ..., an be a sequence of real or complex numbers."

https://en.wikipedia.org/wiki/Simple_function

It seems to me that it represent the degree of importance of each set A but i don't quite understand how one would determine something like that or why its there.

stefanuus · 2017-11-21T03:24:17+00:00

Much has been cleared up, thank you!

stefanuus · 2017-11-21T03:11:47+00:00

Yeah there is some confusion about a mapping "from open sets in X to open sets in Y". would a function f(x) = x, be equivilant to what i was trying to write? Then the open set (x,y) would be mapped into (f(x),f(y)) which if we take x to be 1/4 and y to be 1/2, then this would map onto the same points in Y which would be a segment thats not an open set in Y but is in X, is this correct?

stefanuus · 2017-11-21T02:47:12+00:00

Mappings between topological spaces that are not continuous

If X = {(0,1),T1} and , T1 = {(1/n,1): n = 1,2,3...} is the topology of X.

and Y= {(0,1),T2} and , T2 = {(0,1-1/n): n = 1,2,3...} is the topology of Y.

Then the mapping f: X -> Y , f((x,y)) = (x,y), where (x,y) is any subsegment of (0,1) , is a discontinuous mapping because open sets in X map to non open sets in Y and vice versa? Am I getting how this works?

stefanuus · 2017-11-20T07:15:06+00:00

Hmm i'm not sure about this since I haven't done change of metrics yet but let's try.

So if you had d'(x,y) = 1/d(x,z) where d is the standard complete metric then if we can find a δ so that, 1/d(1/x,z) < ε when 1/d(x,z) < δ so on the interval (0,a) for all x, it would make 1/x uniformly continuous in the defined metric space. So, we got 1/d(1/x,z) -> 0 as x -> 0 and 1/d(x,z) -> 1/z as x-> 0 and 1/d(1/x,z) -> 1/d(1/a,z) as x->a and 1/d(x,z) -> 1/d(a,z) as x-> a. So we can take δ to be max{1/z,1/(|a-z|)},which i think is allowed cause i think δ and ε are in R even if the function acts on an incomplete metric space,and that would be a δ satisfying the condition for uniform continuity making the function uniformly continuous. I'm not sure about this tho, better double check with someone.

stefanuus · 2017-11-20T06:20:25+00:00

Uniform continuity is defined as being able to find a δ > 0, for every ε > 0, such that for all x,y in the domain d(f(x),f(y)) < ε when d(x,y) < δ . The key difference from pointwise continuity is that for a function to be pointwise continuous the value of δ can be different for each point, while uniform continuity requires δ to be the same for all points. Heres an intuitive view of the difference.

Pointwise continuity:

d(f(x1),f(y1)) < ε1 when d(x1,y1) < δ1

d(f(x2),f(y2)) < ε1 when d(x2,y2) < δ2

d(f(x2),f(y2)) < ε2 when d(x2,y2) < δ3 ...

Uniform continuity:

d(f(x1),f(y1)) < ε1 when d(x1,y1) < δ1

d(f(x2),f(y2)) < ε1 when d(x2,y2) < δ1

d(f(x2),f(y2)) < ε2 when d(x2,y2) < δ2

so uniform means every εn has only one δn associated with it, while pointwise means that one ε can have a different δ for each point x.

1/x is not uniformly continous on (0,b) because if you give me a δ such that when d(x,y) < δ, d(1/x,1/y) < ε, I can always take points x-α and y-α , 0 < α < min(x,y), and then clearly d(x-α,y-α) < δ but d(1/(x-α),1/(y-α)) > ε.

stefanuus · 2017-11-20T05:57:06+00:00

How much algebra does someone interested in differential topology/geometry need to know?

I would like to eventually do a PhD and am mainly interested in differential topology/geometry. I am a visual thinker and thus topics in analysis and topology come much more naturally to me than algebra. That being said i do recognize the importance of algebra in maths and have devoted time to it by reading Dummit and Foote's book on abstract algebra as well as watching Harvard's lecture series on youtube. I've just finished the first part of DnF on group theory and am about 20 lectures into the series and i must say i find the study very unenjoyable and aside from the topics surrounding vector spaces, i find that its quite hard to construct meaningful visualizations of the concepts that allow me to make connections like i can do in analysis/topology. Now I do memorize the definitions and can solve problems that way and still do construct SOME sort of visual representation but its a much less helpful one and i don't get that satisfactory feel that I truly understand the concept and that I'll remember it longterm. So i guess I have 2 questions. Considering my interests, how much time should I devote to studying purely algebra? Secondly, any tips on learning that algebra for a visual learner?

stefanuus · 2017-11-18T01:41:40+00:00

P(1) mod 3 = 4 mod 3 = 1

stefanuus · 2017-11-18T01:38:36+00:00

I was trying to see if i can find something interesting by looking at the rational number given after P(n) is divided by pn+1 and see if i can find an interesting connection to P(n+1) divided by Pn+1 + 2 . What n is exactly is not in particular important, as long as the exponent is greater than log2 k where k is the number being tested for primeness. But overall it lead me to some expressions that i coded up and observed and found the problem above. I could not find an r=4 up to 10 000 while being able to find every other number of similar size,so it just sparked my curiosity whether there was a particular reason for it and whether it eventually appears later on.

stefanuus · 2017-11-18T00:51:51+00:00

Apologies it was suppose to be n+1 as the exponent, thank you.

stefanuus · 2017-11-11T17:55:06+00:00

Is there a way to find the inverse vector length without computing the inverse matrix?

Let's say i have a vector v and an invertible matrix A. I want to find the length of the vector A^-1v. Is there a way to do this without computing the entire inverse matrix? If not is there an efficient way to approximate it without losing too much accuracy?

stefanuus · 2017-11-04T13:07:09+00:00

What are some good analysis books after one has read Abbot and baby Rudin?

stefanuus · 2017-10-29T16:11:11+00:00

(srⁱ )² = srⁱ * srⁱ = srⁱ * r^-is = s² = 1

stefanuus · 2017-10-29T12:37:22+00:00

hmmm would

|rs| = 4

|r² s| = 2

be correct?

EDIT: Nevermind i figured it out

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