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Nov
22
comment How can I prove this language is not regular?
@sam: Think a bit more about the hint that I gave; it contains the key idea. If you keep increasing in steps of size $s$, you have to hit numbers that are between powers of $2$, because after a certain point all powers of $2$ are more than $s$ units apart.
Nov
22
comment Defining a Perplexing Two-Dimensional Sequence Explicitly
@teadawg1337: You’re very welcome!
Nov
22
answered How can I prove this language is not regular?
Nov
22
comment How can I prove this language is not regular?
Either the pumping lemma for regular languages or the Myhill-Nerode theorem will do the job fairly easily; are you familiar with either of them?
Nov
22
revised How can I prove this language is not regular?
MathJax
Nov
22
answered Defining a Perplexing Two-Dimensional Sequence Explicitly
Nov
22
answered How to know if a term is divisible by 10
Nov
22
answered Completely regular space with a G$_\delta$-singleton which is not a zero-set
Nov
22
answered How I can explain this contradiction regarding the number of elements in a set
Nov
22
answered quotient graph $G^R$
Nov
22
comment What is $\Gamma(a)$?
Thanks, @bof; I was too lazy to go out to the other room to find the book and check.
Nov
22
comment Will every continuous map from $S^1$ to itself have a fixed point?
@learnmore: Rotate the circle through a right angle around its centre. Is that a continuous map? Does it have a fixed point?
Nov
22
comment For $\sum = \{ 0,1 \}$, $A$ has strings which contain a $1$ in their middle third, and a $B$ which contain two $1$'s in their middle third.
@Harshal: You’re welcome!
Nov
22
comment Understanding the mechanics of P-adic topologies
You’ve misinterpreted $\Bbb Z_p$: it’s not $\Bbb Z/p\Bbb Z$, which is how you seem to be interpreting it, but rather the set of $p$-adic integers, whose members can be thought of as the infinite sums $\sum_{k\ge 0}a_kp^k$ with all $a_k\in\{0,\ldots,p-1\}$. For $p=3$, then, $U_2(1)$ takes each $\sum_{k\ge 0}a_k3^k$, multiplies it by $3^2$ to get $\sum_{k\ge 2}a_{k-2}3^k$, and adds $1$.
Nov
22
answered What is $\Gamma(a)$?
Nov
22
comment For $\sum = \{ 0,1 \}$, $A$ has strings which contain a $1$ in their middle third, and a $B$ which contain two $1$'s in their middle third.
@Harshal: You should be able to show that if you take any word of the form $u1v$, where $u$ and $v$ are non-empty, you can write it in the form $xyz$, where $|x|=|z|\ge|y|$, and $y\in\Sigma^*1\Sigma^*$. HINT: If $|u|\le|v|$, take $z=v$, and if $|u|<|v|$, take $x=u$.
Nov
22
comment Understanding the mechanics of P-adic topologies
To get the curly braces, use \{ and \}.
Nov
22
revised Understanding the mechanics of P-adic topologies
Fixed MathJax.
Nov
22
comment Infinite prisoners with hats — is choice really needed?
@Asaf: Just wait: the day will come when things that you remember as having happened just a few years earlier are ancient history to your students and young colleagues!
Nov
22
comment For $\sum = \{ 0,1 \}$, $A$ has strings which contain a $1$ in their middle third, and a $B$ which contain two $1$'s in their middle third.
@Harshal: That will work fine, but you can cut it down to $X\to 0\mid 1\mid 0X\mid 1X$ without losing anything.