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I'm a student of mathematics in Germany.


Apr
18
answered Classical geometry statement in modern terminology
Apr
14
comment compact open set?
Every compacet set in a metric space (or more generally a Hausdorff space) is closed in it. You certainly implied this, but I think it’s worth stating it explicitly.
Apr
13
comment Simply Connected Points in Disk
Do you mean $S^1$?
Apr
11
comment Is the length of the composition series of a free module identical to the number of its bases?
Thank you. I have the same issue (and therefore the same wording).
Apr
11
comment Is the length of the composition series of a free module identical to the number of its bases?
Can you tell me on which page you have found this? And can you tell me which version of Commutative Algebra you have? So I can look up to see if I have the same wording.
Apr
11
comment Is the length of the composition series of a free module identical to the number of its bases?
Okay, it seems to me that you are right. For $λ(M) = l(M)/l(A)$ it’ll work, though, wouldn’t it?
Apr
11
comment Is the length of the composition series of a free module identical to the number of its bases?
What are the $A_n$?
Apr
11
revised Finding the CFG (Context Free Grammar) of a language
edited body
Apr
11
comment Finding the CFG (Context Free Grammar) of a language
@danishjo It’s a trivial statement, of course, but it should help you thinking about the variables you have to introduce and which rules to apply to them. Did you already try to construct a grammar?
Apr
11
answered Finding the CFG (Context Free Grammar) of a language
Apr
10
comment How could I have found the closed form of $\sum_{k=1}^n \frac{k}{(k+1)!}$ in advance?
Thank you for this very enlightening answer – upvoted. Out of curiosity: Why is it that you speak about yourself as “we”?
Apr
10
accepted How could I have found the closed form of $\sum_{k=1}^n \frac{k}{(k+1)!}$ in advance?
Apr
10
comment How could I have found the closed form of $\sum_{k=1}^n \frac{k}{(k+1)!}$ in advance?
Well, yeah. Exactly what I was looking for. Thank you.
Apr
10
asked How could I have found the closed form of $\sum_{k=1}^n \frac{k}{(k+1)!}$ in advance?
Apr
9
comment Definition of field extension
You’ll have to keep track of all the morphisms and all the different fields. Other than that, it’s a generalization and has all the classical advantages and disadvantages of generalizations: Some definitions, concepts and proofs become clearer, and with others you have to be more careful. For example, naturally a intermediate extension of $E/F$ would be an extension $L/F$ such that $E/L$ is an extension, too. Now, discerning these intermediate extensions becomes more subtle. And how can you talk about the “number” of intermediate extensions? One has to be more careful.
Apr
9
comment Continuity of the sum of continuous functions
@Jens Well, you can redo the proof that the composition of continuous functions is continuous for your special case. This is sort of only using the preimage definition.
Apr
9
comment Continuity of the sum of continuous functions
This is only true if $f$ is continuous. So show instead that the absolute value $ℝ → ℝ,\; x ↦ |x|$ is continuous. (Well, this actually is almost the definition of the topology of $ℝ$.) Then $|f| = |·| ∘ f$.
Apr
9
comment Determining injectivity and surjectivity
Try to write an integer in two different ways using the functions respectively – if this is possible, the respective function is not injective. Try to find an integer which you cannot write using the functions respectively – if you find one, the respective function is not surjective. Also, think of unique prime factorization.
Apr
9
revised Determining injectivity and surjectivity
added 10 characters in body
Apr
9
revised Determining injectivity and surjectivity
edited tags