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Nov
11
revised Fibonacci Proof: Prove that $\frac{F_n-F_{n+16}}{7}$ is always an odd integer.
Mising parenthesis, better formatting.
Nov
11
answered Prove that symmetric closure of R $h_{sym}(R) = R \cup R^T$
Nov
11
answered An implication involving filters
Nov
11
answered Explain why the following collection of sets does not have a system of distinct representatives
Nov
11
revised An implication involving filters
Readability.
Nov
11
comment Monotonic subsequences
@Mary: If you did it right, you found that it’s increasing on one side of a certain number $\alpha$ and decreasing on the other side. Show that if $x<\alpha$, then $f(x)<\alpha$, and if $x>\alpha$, then $f(x)>\alpha$.
Nov
11
comment An implication involving filters
It doesn’t make sense. If $x\in I\cup J$, then $x$ is a filter. If $K\in z$, then $K$ is a subset of $U$. Possibly $K\in x$, but not $K\subseteq x$.
Nov
11
answered Monotonic subsequences
Nov
11
comment If $L \cdot \{\epsilon, a, b\}$ is regular, is $L$?
@TheNotMe: $|\alpha|$ is the length of the word $\alpha$. Hagen is saying that you can choose a set $A$ of even natural numbers so that the set of words over $\{a,b\}$ whose lengths are not in $A$ is not regular. But then every word over $\{a,b\}$ of odd length will be in $L$, so every word of positive even length will be $\alpha a$ or $\alpha b$ for some $\alpha\in L$, and $L\cdot\{\epsilon,a,b\}$ will be $\{a,b\}^*$. (You have to make sure that $0\notin A$, or you get only $\{a,b\}^+$.)
Nov
11
comment Measuring water puzzle
See the references in my answer to this question; one of them is to a web site.
Nov
11
answered Funções/Sequências (Functions/Sequence)
Nov
11
comment Funções/Sequências (Functions/Sequence)
I may be able to, but I need to think about it a little more to be sure.
Nov
11
comment Funções/Sequências (Functions/Sequence)
You’re welcome; Google translate did a pretty good job this time, so I just fixed a couple of little things.
Nov
11
revised Funções/Sequências (Functions/Sequence)
added 3 characters in body; edited tags
Nov
11
answered $[\![n]\!]\times[\![m]\!]\sim[\![nm]\!]$ where $[\![n]\!] = \{1,\ldots,n\}$
Nov
11
comment If $L \cdot \{\epsilon, a, b\}$ is regular, is $L$?
It’s not true that there must be $3$ accepting states; there could be more or fewer.
Nov
11
answered Help needed with complements, partition and power sets
Nov
11
answered I have been asked this particular number theory question in an interview.
Nov
11
comment Induction proof of a recurrence relation
I suspect that the problem is badly worded, and that your combinatorial argument is what is actually wanted. Although it’s not a proof by induction, it is a proof of a recurrence, and the two ideas are sometimes confused.
Nov
11
comment Proving that the axiom of choice implies the well ordering principal
If you right-click on the definition of $F(\alpha)$ and select Show Math As > TeX Commands, you’ll see how you can define multipart functions without using a matrix.