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Oct
31
answered Proving that $\Bbb{R}_\ell$ is finer than $\Bbb{R}$.
Oct
31
comment For each pair in the list decide with proof if the groups are isomorphic
@Emily: Yes, it is, so $C_4\times C_3$ is isomorphic to $C_{12}$. Now look at $\langle a,b\rangle\in C_2\times C_6$. What do you get if you add together six copies of it?
Oct
31
comment For each pair in the list decide with proof if the groups are isomorphic
@Emily: You don’t have separate groups $C_4$ and $C_3$; you do it in the group $C_4\times C_3$. $\langle 1,1\rangle+\langle 1,1\rangle=\langle 2,2\rangle$; $\langle 2,2\rangle+\langle 1,1\rangle=\langle 3,0\rangle$; $\langle 3,0\rangle+\langle 1,1\rangle=\langle 0,1\rangle$; and so on.
Oct
31
answered Weierstrass… thing
Oct
31
comment Orthogonal Matrix statements/proofs
Do you know that $Q$ is orthogonal if and only if $Q^{-1}=Q^T$?
Oct
31
revised Orthogonal Matrix statements/proofs
LaTeX.
Oct
31
comment For each pair in the list decide with proof if the groups are isomorphic
@Emily: Which part? The first is just a matter of adding $\langle 1,1\rangle$ to itself repeatedly to see how long it takes to reach $\langle 0,0\rangle$.
Oct
31
answered For each pair in the list decide with proof if the groups are isomorphic
Oct
31
comment How to weigh up to 100kg with 5 weights
@Chris: The system is known as balanced ternary.
Oct
31
answered Find probability that only one event will occur
Oct
31
comment partition demonstration
@David: You’re welcome!
Oct
31
comment partition demonstration
@David: I’d look at it a little differently: you’ve proved that if $A_x\cap A_y\ne\varnothing$, then $A_x=A_y$, so if $A_x\ne A_y$, then $A_x\cap A_y=\varnothing$. That almost completes the demonstration: you do still have to demonstrate that these sets cover $\Bbb R$, but this is trivial, since $x\in A_x$ for each $x\in\Bbb R$.
Oct
31
answered partition demonstration
Oct
31
comment Find the number of positive integers whose digits add up to 42
@tohecz: No, but it’s an answer to the question. I judge each question individually to determine what sort of answer seems most appropriate. Sometimes it’s a complete solution to the problem; often, especially with elementary questions, it’s a push in the right direction, though I tend to give bigger hints than some others. I also try to take into account the level of knowledge of the OP, if there’s any indication of it.
Oct
31
comment Find the number of positive integers whose digits add up to 42
@tohecz: No, only if the OP tags it that way or says explicitly in a comment that it is homework.
Oct
31
comment Find the number of positive integers whose digits add up to 42
@tohecz: On the contrary, when taken with the linked material it does most of the work. In any case it’s not intended to be complete; indeed, it’s intended not to be complete. It’s intended to give the OP enough information to finish solving the problem, while still leaving some work to be done. Many of us prefer not to give complete solutions to problems that are standard undergraduate course material, especially when the OP actually asks for hints. Most people learn more when they do at least some of the work themselves.
Oct
31
comment Designing Context-Free Grammars for Sets of Strings
You’re welcome.
Oct
31
comment Does this function satisfy “Intermediate Value Property”?
Graphing the function would be a good first step; the picture leads fairly easily to counterexamples like the one that tetori gives.
Oct
31
comment Designing Context-Free Grammars for Sets of Strings
Yes, you need to list all of the non-terminals.
Oct
31
comment Designing Context-Free Grammars for Sets of Strings
That looks much better. Whether you can get away with giving only the productions and the initial symbol instead of giving the complete description depends on the instructor. If in doubt, give the whole thing.