# Panther

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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 .

# 166 Questions

 6 Why is continuity of individual functions essential in Dini's theorem? 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 $[F(a):F(a^3)] \leq 3$

# 1,596 Reputation

 +10 Why is continuity of individual functions essential in Dini's theorem? -2 Algebraic multiplicity of an eigenvalue -2 contradicting identity theorem? -2 Algebraic multiplicity of an eigenvalue

 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 general-topology × 26 3 trigonometry 1 linear-algebra × 15 2 abstract-algebra × 92 1 elementary-number-theory × 4 2 group-theory × 44 1 vector-spaces × 2 1 real-analysis × 60 1 adjoint

# 18 Accounts

 Mathematics 1,596 rep 1516 Academia 131 rep 4 Meta Stack Exchange 101 rep 1 Cross Validated 101 rep 2 TeX - LaTeX 101 rep 2