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Let $k_1, k_2, k_3$ be natural non-negative numbers such that $k_1+k_2+k_3=K$. Let $n_1, n_2, n_3 in {0, ldots, N}$ and such that $n_1+n_2+n_3=N$. Calculate $$...
Asked on 01/05/2022
0 answerSuppose $M,N$ are manifolds, and consider the product $Mtimes N$.From this answer, I know that: $T_{(m,n)}(M times N) cong T_m M oplus T_n N $Can we conclude that...
Asked on 01/05/2022
1 answerThis may be a simple question, but I was slightly confused. I was looking at the second line $S_n(x)=1-x^{n+1}/(1-x)$. I was confused how they derived this. I...
Asked on 01/05/2022
5 answer(Note: I'm only an amateur in logic, so I'm sorry for any weirdterminology or notation, or excessive tedious details. Most of what Iknow is from Kunen's Foundations...
Asked on 01/05/2022
1 answerLet $(X,T)$ and $(Y,T')$ be two topological spaces and $Asubset X ,Bsubset Y$.Show that $$(A^ctimes B)cup(Atimes B^c)cup(A^c times B^c)=(A^ctimes Y)cup(Xtimes B^c)$$solution $$1...........(A^ctimes B)cup(Atimes B^c)cup(A^c...
Asked on 01/05/2022 by Yahya B. Jaber
1 answerFor the following question,$$mathbf{F}=langle-y, xrangle$$For this field: Compute the line integral along the path that goes from (0,0) to (1,1) by first going along the ...
Asked on 01/05/2022
3 answerThis is exercise 6, part b of Practice exercises of chapter 6 of PD Magnus forallx Introduction to formal logic I am not sure if I used correctly the disjunction...
Asked on 01/05/2022 by Mauricio Vega
2 answerI need to study the convergence of the following improper integral: $$int_{0}^{infty} dfrac{sin(x)}{x+1}, mathrm dx$$ I did the following: $$ -1 leq sin(x) leq 1 \...
Asked on 01/05/2022 by Kirito
4 answerI am trying to determine a systematic way to find all the integer vales of $a$ such that $a^2 - 4a$ is a perfect square. If it...
Asked on 01/05/2022 by hardik-ddod
3 answerenter image description hereCan someone help me to solve this equation:$$y^2-2ln(y)=x^2$$I want to find y.I have tried to solve the problem but I...
Asked on 01/05/2022 by Majdgh
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