Proof completeness of $L^p$

The only mistake I see is where you claim that $|f|\leq|f_{n_1}|+|g|$ implies $|f|^p\leq|f_{n_1}|^p+|g|^p$ , which is not true ($1\leq1/2+1/2$ does not imply $1^2\leq (1/2)^2+(1/2)^2$). What you have to use is that the sum of two functions in $ L^p $ is again in $ L^p $.

Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$

Triangular series perfect square formula 8n+1 derivation

Covariant derivative for higher rank tensors

Is showing $\lim_{z \to \infty} (1+\frac{1}{z})^z$ exists the same as $\lim_{n \to \infty} (1+1/n)^n$ exists

Pigeonhole principle: prove that any set of $n+1$ integers from $\{1,2,...,2n\}$ has two consecutive integers differ by one.

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Prove $\int_{a}^{b}{f(x)dx}>0$.

Minimal polynomial of intermediate extensions under Galois extensions.

if G is generated by {a,b} and ab=ba, then prove G is Abelian

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Change Makefile variable value inside the target body