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 Oct 21 comment How do I prove that the following is a presentation of $\mathbb{Z_{35}}$? Thank you so much for your detailed response. I will take my time to read carefully your answer, and write back if there were any questions. Thanks again. Sep 21 comment How do I find a (7, 3) parity check code generator matrix? I came up with another matrix using $p(x) =1+x+x^3+x^4$ $$G=\pmatrix{1&0&0&1&1&0&1\cr0&1&0&1&0&1&1\cr0&0&1&1&0&0&0\cr}$$ Would this also be correct? I'm confused about the polynomials one chooses and I didn't find any literature that I could understand addressing this problem. Sep 21 comment How do I find a (7, 3) parity check code generator matrix? I 'll do that now. :) Thanks again. Sep 21 comment How do I find a (7, 3) parity check code generator matrix? Thanks for your answer. Would the explanation for how you came about constructing the matrix also be there? 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 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 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 $x \in A$. 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 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 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. 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? Sep 23 comment How do I show $|\frac{i\overline{z}}{2} - \frac{i}{2}|=|z - 1|?$ @Timbuc I didn't. And thanks for your help. Sep 23 comment How do I show $|\frac{i\overline{z}}{2} - \frac{i}{2}|=|z - 1|?$ @Timbuc No, only that $|Z| < 1$ Sep 23 comment How do I show $|\frac{i\overline{z}}{2} - \frac{i}{2}|=|z - 1|?$ So, it's a mistake in the text? Sep 23 comment How do I show $|\frac{i\overline{z}}{2} - \frac{i}{2}|=|z - 1|?$ Of course I tried that before asking here. This isn't my homework, btw. May 17 comment Connected spaces: is there a mistake in the example below from James Munkres' Topology? Thank you for your answer. May 17 comment Connected spaces: is there a mistake in the example below from James Munkres' Topology? Yes, you're right. I was skipping over the word 'contains'. And, no it doesn't say that the subspace is connected. Lots of confusion in my head, is all. Thanks for your help.