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usukidoll
  • Member for 10 years, 4 months
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8 votes
2 answers
9k views

$R$ is transitive if and only if $ R \circ R \subseteq R$

8 votes
3 answers
4k views

Which rational primes less than 50 are also Gaussian primes?

6 votes
2 answers
3k views

Determining which pairs of quantified statements are equivalent

5 votes
5 answers
884 views

Prove that the inequality $(1+ \frac{1}{n})^n < n$ holds for all $n \geq 3$

5 votes
2 answers
435 views

Prove or disprove $(A + B) \cap C = (A \cap C) +(B \cap C)$

5 votes
1 answer
1k views

Proving isomorphisms from posets.

5 votes
0 answers
210 views

Arithmetic Functions: Evaluate $ \sigma(210)$ and $d(63)$

5 votes
3 answers
4k views

Let $a,b \in R$ where $ a < b$. Prove that there exist a rational number $c$ and an irrational number $d$ such that $ a <c<b$ and $ a<d<b$.

4 votes
1 answer
682 views

On $N \times N $ define the relation R, setting $(a,b),(c,d) \in R$ if and only if $a+d=b+c$. Show that $R$ is an equivalence relation.

4 votes
4 answers
7k views

Prove for all $n \in N$, $\gcd(2n+1,9n+4)=1$

4 votes
2 answers
431 views

Find the particular solution of $u_x+2u_y-4u=e^{x+y}$ satisfying the following side condition $u(x,-x) = x$

3 votes
1 answer
118 views

PDEs with Variable Coefficents: Solve $xu_x-xyu_y-u=0$ for all $ (x,y)$

3 votes
3 answers
2k views

Solve the 3 Dimension first order PDE $xu_x+yu_y+zu_z=0$

3 votes
0 answers
500 views

Proving the Maximum Principle and the Continuous Dependence on Initial Condition and Boundary Conditions.

3 votes
0 answers
211 views

Prove $f_\infty: A_\infty \rightarrow B_\infty$ is a bijection

3 votes
1 answer
872 views

Composite Relations - Give Examples of relations $R_1$ and $R_2$ such that $R_2 \circ R_1 = R_1 \circ R_2$ and $R_2 \circ R_1 \neq R_1 \circ R_2$

3 votes
1 answer
486 views

Find a solution to Laplace's equation that satisfies polar coordinates and show that any solution produces perpendicular lines.

3 votes
3 answers
10k views

Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $

3 votes
2 answers
1k views

If $A \subset R^{n}$ is not closed, show that there is a continuous function $f: A \rightarrow R$ which is unbounded.

3 votes
1 answer
52 views

There are 3000 students each taking exactly 4 courses and there are 803 courses being offered. How big could the smallest class be?

3 votes
2 answers
835 views

Using Normal and Binomial approximations for airline tickets

2 votes
3 answers
366 views

Show that $\alpha$ is a bijection.

2 votes
1 answer
2k views

Prove the following statement: If A is any set, then $A \subseteq A$

2 votes
1 answer
5k views

Flux across the circle

2 votes
1 answer
2k views

Solve for an Undetermined Coefficent by using annihilator method.

2 votes
1 answer
572 views

Variation of parameters for a linear second order nonhomogeneous equation

2 votes
1 answer
331 views

Laplace Transformation Proof - Show that $L\{f_a(x) \} = \hat f(s+a)$

2 votes
5 answers
233 views

Prove that $A \ne B$ is equivalent to the logical statement $(\exists x)[x \in A \land x \notin B] \lor (\exists x)[x \in B \land x \notin A]$

2 votes
1 answer
1k views

Prove $A+ \emptyset = A, A+A = \emptyset$, and $A +A' = U$ using the definition of $A+B$

2 votes
4 answers
416 views

For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$