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### Questions (335)

 12 Understanding why the empty set is closed 10 The Main Theorems of Calculus 5 Give an example such that $(x_ny_n)$ converges but $(x_n)$ and $(y_n)$ diverges. 4 Prove that $X\times Y=\emptyset$ $\iff$ $X=\emptyset$ or $Y=\emptyset$. 4 Show that there is no other isomorphim

### Reputation (1,551)

 +5 The sum of the first n odd natural numbers +10 A Question of Ordinal - İnitial Segment +5 Show the relation well-orders $S$ +5 Is it true that union of an increasing chain of well-ordered sets is well-ordered?

 1 Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$. 1 Show that $5\mathbb{Z}+3\mathbb{Z}=\mathbb{Z}$ 1 Show that $5 \mathbb{Z} +8= 5\mathbb{Z} +3= 5\mathbb{Z} +(-2)$. 1 Requesting abstract algebra book recommendations 0 Suppose $a,b\in\mathbb{Z}$. If $a^2(b^2-2b)$ is odd, then $a$ and $b$ are odd.

### Tags (65)

 2 elementary-set-theory × 124 0 proof-writing × 40 1 elementary-number-theory × 13 0 analysis × 39 1 ring-theory × 2 0 proof-verification × 24 0 linear-algebra × 81 0 calculus × 16 0 real-analysis × 69 0 analytic-geometry × 16

### Accounts (7)

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