# VHP

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An Engineer turned student of Theoretical Mathematics.

I mostly try to self teach myself. Love Abstract Sciences and just love this site.

A Theoretical Research Mathematician one day .

# 167 Questions

 6 Prove that the zeros of an analytic function are finite and isolated 4 $\int_{0}^{\infty} f(x) \,dx$ exists. Then $\lim_{x\rightarrow \infty} f(x)$ must exist and is $0$. A rigorous proof? 4 If $f: \mathbb R^2 \rightarrow \mathbb R$ is a continuous function such that $f(x)=0$ for only finitely many values of $x$, [duplicate] 4 Let $K$ be a field extension of $F$ and let $a \in K$. Show that $[F(a):F(a^3)] \leq 3$ 4 Show that an integral domain with every strictly decreasing chain of ideals $I_1 \supset I_2\supset \cdots$ finite in length is a field. [duplicate]

# 1,592 Reputation

 +5 Prove that the field of quotients of an integral domain $D$ is the smallest field containing $D$. . My Attempt Shown +5 Prove that the zeros of an analytic function are finite and isolated +5 How many homomorphisms $\Psi : S_3 \rightarrow S_3$ exist? +5 If $f$ is continuous on $[0,1]$ and if $\int_0 ^1 f(x) x^n dx = 0$ for $n=0,1,2,3,\cdots$; then prove or disprove $\int _0 ^1 f^2(x) dx = 0$

 3 How can the circular function $\tan(\theta)$ be both a length and a ratio of lengths? 2 $T$ is normal if only if for all subspace T-invariant, the complement orthogonal is T-invariant. 1 Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra 1 How to evaluate $\lim_{x \to \infty}\left(1 + \frac{2}{x}\right)^{3x}$ using L'Hôpital's rule? 1 Proof needed for this exercise from “Linear Algebra Done Right”

# 67 Tags

 3 algebra-precalculus × 2 1 real-analysis × 61 3 trigonometry 1 general-topology × 26 2 abstract-algebra × 92 1 elementary-number-theory × 4 2 group-theory × 44 1 vector-spaces × 2 2 linear-algebra × 15 1 adjoint

# 17 Accounts

 Mathematics 1,592 rep 1415 Academia 126 rep 4 Meta Stack Exchange 101 rep 1 Cross Validated 101 rep 2 TeX - LaTeX 101 rep 2