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 Yearling
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  • 29 votes cast
Jul
28
comment Can an interval be represented as a set?
Yes, intervals are sets, $A_n = \{x \in \mathbb{R} : 0 \le x \le n\}$ and $A = \{x \in \mathbb{R} : x \ge 0\}$. You can apply the theorem previously proved.
Jul
25
revised Why are the sets $U_x$ disjoint in this proof of the non path-connectedness of the ordered square, $I_0^2$?
added 10 characters in body
Jul
25
comment Why are the sets $U_x$ disjoint in this proof of the non path-connectedness of the ordered square, $I_0^2$?
@BrianM.Scott Thanks for the correction. I'd forgotten exactly what it meant for a set to be well-ordered at the time.
Jul
24
answered Why are the sets $U_x$ disjoint in this proof of the non path-connectedness of the ordered square, $I_0^2$?
Jul
22
awarded  Yearling
Jul
22
comment Does anyone understand this proof: If $A$ is closed and bounded $\implies A$ is sequentially compact.
@BozoVulicevic $A$ is closed iff $x_n \in A$ and $x_n \to x$ implies $x \in A$.
Jul
22
answered Does anyone understand this proof: If $A$ is closed and bounded $\implies A$ is sequentially compact.
Jun
21
accepted How does one construct the Galois field extension $GF((2^2)^3)$?
Jun
21
comment How does one construct the Galois field extension $GF((2^2)^3)$?
Thank you for answering. I have a question, why is it that $-1 = 1$, when I was doing the calculations by hand yesterday, I was using $-3=1$, and I had $\beta^3=3 \alpha \beta^2 + 3\alpha \beta + 3 \alpha$. Also, how do you find the inverse of $\alpha$, and then how exactly does $\beta^4= \beta^2 + \beta + \alpha^2$? If you can help with the relations of the elements in the coefficient field, then I think I'll be able to do the calculations.
Jun
20
comment How does one construct the Galois field extension $GF((2^2)^3)$?
@JyrkiLahtonen I don't think we're being asked to check if the polynomial is indeed primitive. I don't know very much yet, but I'm thinking the problem is to write down/find explicitly every element of the finite field as a linear combination of the basis elements of the corresponding cyclic group when, say, $\beta$ is the primitive element. I tried doing that and after very tedious computations wasn't able to show that $\beta^{63}=1$.
Jun
20
comment How does one construct the Galois field extension $GF((2^2)^3)$?
@ZevChonoles Yes.
Jun
20
revised How does one construct the Galois field extension $GF((2^2)^3)$?
deleted 4 characters in body
Jun
20
comment How does one construct the Galois field extension $GF((2^2)^3)$?
@PatrickDaSilva I was typing the problem as was written, but yes what you wrote is what is meant.
Jun
20
asked How does one construct the Galois field extension $GF((2^2)^3)$?
Jun
7
comment How do I show that the following is a basis for the weak topology on $X$?
@BrianM.Scott Yes, that's what I meant. Apologies, I was typing from my phone and wasn't careful.
Jun
7
comment How do I show that the following is a basis for the weak topology on $X$?
@ThomasE. The definition I'm using is that the topology on $X$ defined by the semi norm $\{pf : f \in X^*\}$ is the weak topology.
Jun
7
revised How do I show that the following is a basis for the weak topology on $X$?
added 6 characters in body
Jun
7
asked How do I show that the following is a basis for the weak topology on $X$?
May
4
asked Is there an easy proof to this theorem due to Nagata?
May
3
comment How do I solve this PDE (diffussion equation) using the sepration of variables method?
Can I ask where is this taken from so that I may look it up in the library here?