# Spenser

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Third year undergraduate student in mathematics.

 11 Great contributions to mathematics by older mathematicians 7 If $f(x)+2f(1/x)=3x$, find all $y$ such that $f(y)=f(-y)$. 7 Which is bigger: $\sqrt{1001} - \sqrt{1000}$, or $\frac{1}{10}$? 7 Is the set of decreasing functions from $\Bbb N$ to $\Bbb N$ countable? 6 Lower bound for $2\sin^2(y\pi)$

# 3,275 Reputation

 +15 How to find a continuous function that demonstrates that the set $\{(x,y):y>x\}$ is open? +25 Formalizing a concept of vectors +10 queston about T4- spaces +15 Why is $E[X1_A]=0$ if $P(A)=0$?

# 52 Questions

 16 Show $\int_0^\infty\left(1-x\sin\frac 1 x\right)dx = \frac\pi 4$ 14 Prove the divergence of the sequence $(\sin(n))_{n=1}^\infty$. 14 Sum of reciprocals of primes factorial: $\sum_{p\;\text{prime}}\frac{1}{p!}$ 13 Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$ 12 Examples of nonlinear ordinary differential equations with elementary solutions.

# 75 Tags

 19 sequences-and-series × 9 11 differential-equations × 6 17 algebra-precalculus × 3 9 calculus × 7 13 real-analysis × 15 9 limits × 6 13 linear-algebra × 13 9 analysis × 5 13 integration × 10 9 trigonometry × 3

# 3 Accounts

 Mathematics 3,275 rep 2839 TeX - LaTeX 211 rep 14 Physics 123 rep 5