1HE1C +JDF0= 2H7GC from calculator

By hand I couldn't get the H

Using

1

2

3

4

5

6

7

8

9

A=10

B=11

C=12

D=13

E=14

F=15

G=16

H=17

I=18

J=19

K=20 ]]>

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Show that if $G$ is a finite group, then there are an odd number of elements $g\in G$ for which $g^3 = 1$.

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Remember to read the POTW submission guidelines to find out how to submit your answers! ]]>

Sorry I've been away for a few months now, but now I'm back and will post new POTW soon. See you soon! ]]>

photo_2019-09-14_13-24-12.jpg

1. all 5 dice rolls are the same

2. 4 dice rolls are the same

3. the dice rolls are in sequence (1-5 or 2-6) -order does not matter

4. two pairs of dice are the same (ex: 1 1 4 4 3)

5. the result is one pair and the other three are the same (ex: 1 1 1 6 6)

So far, my understanding of the problem has been the ff:

1. 1/6^5

2. 150/6^5

3.(5!+5!)/6^5

4. 1800/6^5

5. 300/6^5

Is this correct? ]]>

Ok Im a little stumped already because we have 3 variables in this a,x and b

W|A returned $e^{ab}$ but not what the steps are, maybe next....

$\displaystyle bx\lim_{{x}\to{\infty}}\left(1+\dfrac{a}{x}\right)$ ]]>

$$(A)\, 1\quad (B)\, \dfrac{1}{e} (C)\, 0 \quad (D) -e \quad (E)

f\textit{ does not have an absolute maximum value}.$$

I only guessed this by graphing it and it appears to $\dfrac{1}{e}$ which is (B) ]]>

ok this is from my overleaf doc

so too many custorm macros to just paste in code

but I think its ok,,, not sure about all details.

appreciate comments.....

I got ???? somewhat on b and x and u being used in the right places

This is should be a simple one. I know what I'm looking for but I don't know what to call it.

I have a member on PHF that I am talking with and I'd like to know the terminology used in the next two definitions.

1) I want to compactify the real numbers by defining $ \displaystyle - \infty$ and $ \displaystyle \infty$ to belong to the compactified set such that, for any member "a" in the compactified set we have that $ \displaystyle -\infty \leq a \leq \infty$. My model is the "hyperintegers" $ \displaystyle [ -\infty, \text{ ... } -1, 0, 1, \text{ ... } , \infty ] $. I know that the hyperreals also contain infinitesimals but I don't actually need them for the discussion.

2) Can I say that the reals and the compactified real numbers defined above are "locally homeomorphic?"

I don't need to get too deep into either concept, I just need the correct terminology so I can talk about it unambiguously.

Thanks!

-Dan ]]>

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Let $ \displaystyle \prod_{n=1}^{1996} (1+nx^{3n})=1+a_1x^{k_1}+a_2x^{k_2}+\cdots+a_mx^{k_m}$ where $a_1,\,a_2,\,\cdots a_m$ are non-zero and $k_1<k_2<\cdots<k_m$.

Find $a_{1996}$.

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Remember to read the POTW submission guidelines to find out how to submit your answers! ]]>

I'm kind of in a rush because I'll have to go to my classes soon here at USF Tampa, but I had one last problem for Intermediate Analysis that needs assistance. Thank you in advance to anyone providing it.

Question being asked: "Let $A$ be a nonempty set of real numbers which is bounded below. Let $-A$ be the set of all numbers $-x$, where $x$ is an element of $A$. Prove that $\inf A=-\sup(-A)$."

This is what I had so far for a proof: "Let $\alpha =\inf A$. For any $x\in A$, $\alpha \le x$. This implies that $-\alpha \ge -x$ for all $-x\in -A$. This means $-\alpha$ is an upper bound of $-A$. Also, if $-\gamma <-\alpha$ then $-\gamma$ cannot be an upper bound of $-A$ because if it is, then $-\gamma \ge -x$ for all $-x \in -A$. This implies that $\gamma >\alpha$ and that $\gamma$ is a lower bound of $A$, which is not possible since $\alpha = \inf A$."

Please help me out here, since this is the last problem I need help with at this point in time and I would really, really appreciate it. Thanks again in advance! ]]>

For instance 12 has the multiple 7776. ]]>

help.png

Also, I'm a uni freshman who isn't used to the whole concept of proofs, and a lot of what my profs say seem to be a slew of symbols and numbers before they even define anything, but I do the textbook readings and can comprehend those fairly easily. Was anyone on here's transition from high school math to university math a massive jump?

I have an Intermediate Analysis problem that needs assistance. I've really been having a hard time with it. This is what the question says:

"Can it happen that A⊂B (A is a subset of B) and A≠B (A does not equal B), yet sup A=sup B (the supremum of A equals the supremum of B)? If so, give an example. If not, prove why not."

Honestly, I'm not even sure where to begin with proving this, so any help would be greatly appreciated on my behalf. Thank you in advance to anyone that replies. ]]>