7,976 reputation
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bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 24
visits member for 2 years, 5 months
seen yesterday

Postgraduate student at the University of Bath, UK, studying geometry and representation theory. Currently thinking about cluster algebras and related objects.


1d
comment How do I turn my verbal argument into something formal in [Real Analysis]? (proving every compact set is bounded)
I think you mean "If not every compact set on a metric space is bounded...".
1d
comment How do I turn my verbal argument into something formal in [Real Analysis]? (proving every compact set is bounded)
To attempt to answer the second part of the question - if the statements you make in the proof were correct, and the exercise occurs in a context in which they had been proved earlier, then I would say your proof is sufficiently formal as it is.
1d
revised Logarithmic question
edited title
Jul
23
comment Differential function as a linear map.
For part 2), you've described the set slightly inefficiently, because $0$ is itself a constant, so it isn't a special case. You have proved that this set is contained in the kernel; why is it the whole thing?
Jul
23
comment Differential function as a linear map.
This is in many ways the root of your problem; you need to check that $T(f)$ is linear in $f$, so if $f$ and $g$ are two differentiable functions, then $T(f+g)=T(f)+T(g)$ (and something similar for scalars). You shouldn't try to check linearity in the arguments of the functions $f$ and $g$, because it won't hold, as you point out. Said differently, you want to check that $T(f+g)(x)=T(f)(x)+T(g)(x)$, not that $T(f)(x+y)=T(f)(x)+T(f)(y)$ - this second statement says that $T(f)$ is linear, rather than that $T$ is linear, and this won't be true for general $f$.
Jul
22
comment What's a bi-rhombus?
@KaungHtetWaiYan I don't think you have much choice - this is not a standard English word, so nobody other than your teacher can tell you what it means, and without knowing what it means you can't do the project. As somebody commented on another version of this question, the problem may be that "bi-rhombus" is an incorrect translation.
Jul
22
comment What's a bi-rhombus?
Re: close votes - I think this question has (just) enough context, since it just asks for the definition of a word (arguably 874786 is better because it gives the sentence in which this word was encountered), whereas the "duplicate" also asks for a solution to the exercise. (For clarity, this comment is meant as a PSA to people who vote the same way as me and might not have noticed this distinction, rather than as a criticism of people who vote differently.)
Jul
21
revised Subsequences and limit inferior
added 3 characters in body
Jul
21
comment Repeated Irreducible Representations in a representation
If you forget about representation theory for a minute - an $n$-dimensional vector space over $K$ decomposes as $V=V_1\oplus\dotsb\oplus V_n$, where each $V_i$ is isomorphic to $K$. So all of the summands are isomorphic to each other as vector spaces, despite being different subspaces of $V$. Given this, it shouldn't be so hard to believe that you can have a representation $W=W_1\oplus W_2$ with $W_1$ and $W_2$ isomorphic representations, even though $W_1$ and $W_2$ are as disjoint as possible inside $W$.
Jul
18
comment Proof needed for this exercise from “Linear Algebra Done Right”
@Hobbit6094 Careful - you can't have $\operatorname{Null}(ST)\subseteq\operatorname{Null}(S)$ because the first is a subspace of $U$ and the second is a subspace of $V$. But what you actually proved is that $T(\operatorname{Null}(ST))\subseteq\operatorname{Null}(S)$, which, if you think it through carefully and use the Rank-Nullity theorem, is enough to get what you want.
Jul
17
comment What is the name of formula?
If you want a name for that specific function, then there probably isn't one. If you just want a name for this kind of function, then piecewise function is probably the most usual.
Jul
15
revised Is a norm on $R^n$ linear?
deleted 5 characters in body
Jul
15
answered Is a norm on $R^n$ linear?
Jul
15
revised What is $\operatorname{Ass}\operatorname{Ext}^i(M,N)$?
added 145 characters in body; edited title
Jul
11
comment If $A$ is compact and connected, then is $\Bbb R^2\setminus A$ connected?
It's not really a stupid question! But the lesson should probably be to always try out some examples first - Heine-Borel makes it fairly easy to generate lots of them. (Of course, if you didn't have a good handle on what it means to be compact, then generating example might be more problematic, but it seems that you do.)
Jul
11
comment How Max plus algebra is different from conventional algebra?
In a sense, your tag provides an answer to the question - the max-plus algebra gives us a neat way to tropicalize a variety, and then there are various theorems relating properties of the original variety to properties of the tropical variety, which are potentially easier to compute because of the combinatorial nature of the object. I believe there are other applications of max-plus not directly to do with tropical geometry, but I don't know what they are.
Jul
10
comment writing papers: definition in word or formula?
This question might be too opinion-based. I don't have any real preference between the three options. If the set had a more complicated definition, then I would probably be more strongly against C) and more strongly in favour of A). The aim should always be clarity, but this can be extremely subjective.
Jul
10
reviewed Approve suggested edit on writing papers: definition in word or formula?
Jul
1
revised If a voronoi vertex q is an endpoint of a voronoi edge l, then the delaunay polygon dual to q has a delaunay edge dual to l as one of its edges.
added 164 characters in body
Jul
1
revised Counting the number of zeros
edited tags