Question

let $A_1, A_2, A_3, \dots$ be a collection of nonempty sets, each of which is bounded above. $(a)$ Find a formula for $\sup(A_1\cup A_2)$.

score 3.6k · Answer 1 · 2015-09-06 18:58:56

let $A_1, A_2, A_3, \dots$ be a collection of nonempty sets, each of which is bounded above. $(a)$ Find a formula for $\sup(A_1\cup A_2)$.

score 45 · Answer 2 · 2015-09-07 16:24:15

45

Views

Prove that $p\in[144,\frac{8^4}{27}]$ where $p=(8-x)(8-y)(8-z)$

Published on 07 Sep 2015 - 16:24

score 53 · Answer 3 · 2015-09-08 22:20:59

53

Views

Manipulating compound inequalities of supremums and upper bounds

Published on 08 Sep 2015 - 22:20

score 2k · Answer 4 · 2015-09-10 02:50:38

2k

Views

Find the supremum and infimum of {x $\in$ [0,1]: x $\notin$ $\mathbb Q$}. Prove why your assertions are correct

Published on 10 Sep 2015 - 2:50

score 414 · Answer 5 · 2015-09-11 02:49:19

414

Views

Lagrange multipliers - hard one

Published on 11 Sep 2015 - 2:49

score 343 · Answer 6 · 2015-09-11 14:48:24

343

Views

Convergent sequence in a bounded set

Published on 11 Sep 2015 - 14:48

score 335 · Answer 7 · 2015-09-12 02:36:17

335

Views

If $ax+by+cz=k$,prove that the minimum value of $x^2+y^2+z^2$ is $\frac{k^2}{a^2+b^2+c^2}$

Published on 12 Sep 2015 - 2:36

score 296 · Answer 8 · 2015-09-12 06:42:28

296

Views

If $4x^4+9y^4=64$ then what is the maximum value of $x^2+y^2?$ using Lagrange's multiplier

Published on 12 Sep 2015 - 6:42

score 193 · Answer 9 · 2015-09-12 13:17:51

193

Views

Infimum of $(\frac{1}{n}+\cos(\pi n))$ Question

Published on 12 Sep 2015 - 13:17

score 641 · Answer 10 · 2015-09-12 13:59:52

641

Views

The length of an interval covered by an infinite family of open intervals

Published on 12 Sep 2015 - 13:59

score 3.9k · Answer 11 · 2015-09-13 17:47:18

3.9k

Views

If S is a bounded set, then inf(S) and sup(s) belong to the closure of S

Published on 13 Sep 2015 - 17:47

score 106 · Answer 12 · 2015-09-14 16:58:30

106

Views

Proof verification about supremums (not hard stuff)

Published on 14 Sep 2015 - 16:58

score 1.1k · Answer 13 · 2015-09-15 21:16:20

1.1k

Views

Supremum of supremums is equal to the supremum of the union

Published on 15 Sep 2015 - 21:16

score 246 · Answer 14 · 2015-09-16 15:14:19

246

Views

Find $\inf(X)$ and $\sup(X)$ then check by definition of supremum and infimum.

Published on 16 Sep 2015 - 15:14

score 538 · Answer 15 · 2015-09-16 20:58:46

538

Views

If $E\subset F$ then $\inf E\ge\inf F$ and $\sup E\le\sup F$

Published on 16 Sep 2015 - 20:58

List Question

let $A_1, A_2, A_3, \dots$ be a collection of nonempty sets, each of which is bounded above. $(a)$ Find a formula for $\sup(A_1\cup A_2)$.

Prove that $p\in[144,\frac{8^4}{27}]$ where $p=(8-x)(8-y)(8-z)$

Manipulating compound inequalities of supremums and upper bounds

Find the supremum and infimum of {x $\in$ [0,1]: x $\notin$ $\mathbb Q$}. Prove why your assertions are correct

Lagrange multipliers - hard one

Convergent sequence in a bounded set

If $ax+by+cz=k$,prove that the minimum value of $x^2+y^2+z^2$ is $\frac{k^2}{a^2+b^2+c^2}$

If $4x^4+9y^4=64$ then what is the maximum value of $x^2+y^2?$ using Lagrange's multiplier

Infimum of $(\frac{1}{n}+\cos(\pi n))$ Question

The length of an interval covered by an infinite family of open intervals

If S is a bounded set, then inf(S) and sup(s) belong to the closure of S

Proof verification about supremums (not hard stuff)

Supremum of supremums is equal to the supremum of the union

Find $\inf(X)$ and $\sup(X)$ then check by definition of supremum and infimum.

If $E\subset F$ then $\inf E\ge\inf F$ and $\sup E\le\sup F$

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