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8m
comment Proof that $12$ in a row tic-tac-toe is a tie game?
@GarethRees See this answer and note the Open Problems, esp. 5.3.
9m
comment Proof that $12$ in a row tic-tac-toe is a tie game?
@GarethRees Consider ordinary tic-tac-toe on $3\times3$ board. Note that the second player can not block the first player making a row of $3$: 1. a1 b2 2. c3 b1 3. a3 b3 4. a2 and player one has $3$ counters on the $a$-file. Of course player two got $3$ counters on the $b$-file. Player can force a draw in ordinary tic-tac-toe, but only because he can counterattack by threatening to make his own $3$-in-a-row. If the drawing strategy for $9$-in-a-row relied on counterthreats, it would not be clear that it works for $10$-in-a-row.
7h
comment Number of Hausdorff topologies on a set with $100$ elements.
Hmm. I'm pretty sure there's only one topology one a 1-element set. How many Hausdorff topologies are there on a 2-element set? or a 3-element set?
15h
comment Prove that if $A$ is both open and closed, $A=\mathbb R$.
I could be wrong, but I think the OP is asking how to prove that $\mathbb R$ is connected.
1d
comment How to formulate the product of two generating functions without their final terms?
You really want the product to be $\sum_{n=0}^\infty(a_0b_{n-1} + a_1b_{n-2} + ... + a_{n-1}b_0) $ with no $z$? And why start from $n=0$, not $n=1$?
1d
comment Are there only a few 'universally convergent' Taylor Series?
$e^{e^x}$? $\frac{\sin x}x$?
1d
revised In a bit string of length 11, how do you find the probability of even number of zeros?
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Apr
25
comment Borel $\sigma$-algebra defintion question
If you take all subsets of $\mathbb R$, that is a $\sigma$-algebra which is larger than the Borel $\sigma$-algebra; it contains all of the Borel sets and various other sets.
Apr
24
answered Equivalence of countable choice for subsets of the reals and “second countable $\implies$ Lindelöf”
Apr
24
comment Every open cover has a countable subcover (Lindelöf's lemma)
@BrianM.Scott Seems to me even "$\mathbb N$ is Lindelöf" is equivalent to $\mathsf{CC}(\mathbb R)$, is that right?
Apr
19
comment Unique properties of pure Imaginary numbers?
The title says "pure imaginary numbers" but the body of the question says "imaginary numbers". Which is it?
Apr
19
comment Combinations and Permutations - tiling a $52\times 3$ grid with $78$ dominos
Can you explain the answer you got? What does $\binom{78}2$ come from? I guess that means you're picking $2$ of the $78$ dominoes? But what's the point of that if the dominoes are identical?
Apr
19
comment Proof that $12$ in a row tic-tac-toe is a tie game?
@MJD Winning Ways (in the edition that I have) has only two volumes. A drawing strategy for $9$-in-a-row is shown in vol. 2, figure 12 on p. 677. By the way, your a fortiori would be hard to justify. Fortunately, the same strategy works for $n$-in-a-row for all $n\ge9.$ That's because it's purely defensive; it blocks the opponent from making $9$-in-a-row, it does not depend on counterattacking by threatening to make one's own $9$-in-a-row.
Apr
19
comment Proof that $12$ in a row tic-tac-toe is a tie game?
@PeterTaylor According to the rules, the game ends after $\omega$ moves if nobody has made $12$ in a row. One could consider a variant, where play continues into the transfinite as long as there are any unoccupied points, but this is not so popular.
Apr
19
comment Are the rows of a hypothetical truth table with infite propositional variables non countable;
Why would a row of your truth table be uncountable?
Apr
19
revised Link between definitional expansions and definitional extensions.
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Apr
19
revised Link between definitional expansions and definitional extensions.
added 4 characters in body
Apr
19
answered Compact subset of $\mathbb R$ whose Lebesgue measure is non-zero
Apr
18
comment Proof of exchange principle in set theory
@AsafKaragila No reason. I didn't know the policy, and I wasn't sure if I should delete the set-theory tag. For that matter I wasn't sure if the elementary-set-theory tag is appropriate. I'm not sure if "foundation" is included in elementary-set-theory, didn't see it mentioned in the tag wiki. Could you kindly clean up after me by deleting whichever of the two tags should be deleted. Thanks.
Apr
18
revised Proof of exchange principle in set theory
edited tags