The Sphinx's Lair

12:13 AM

And indeed you should. (And obviously you can use some other permutation -- change the second digit of the first number and the first of the second; the fourth digit of the third number and the third of the fourth; etc. Or whatever.)

An observation not always made: the diagonal argument, if you write your numbers in binary, is basically the same thing as Russell's paradox. Think of each number as defining a set of numbers -- the positions where there's a 1. The number we're constructing also corresponds to a set of numbers. "The nth digit is different from the nth number" says "n is in our set iff n isn't in the set labelled n".

If there were only countably many sets of positive integers, then we could label our sets with themselves instead of with the numbers 1,2,..., and then the new set we constructed would contain n iff set n doesn't contain n; that is, it would contain each set iff that set doesn't contain itself; this is exactly what Russell does.

Except that he does it with all sets rather than just sets of positive integers, and so what he proves in effect is that if we think we have a "universe" of all sets then we have to be wrong because here's a way of finding a new one.

AncientSwordRage

12:46 AM

Very clever

I never studied anything like that, but it is fascinating

Avi

1:00 AM

@GarethMcCaughan thanks for this; it was very intuitive!

or rather, it made sense to me on an intuitive level

Sphinx

1:44 AM

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Q: How do I get quinaplus to give me words that are (word_a)* in word_b?

I would like to use the Quinaplus Matcher to look for words that are made from two letter sets, let's call them $word_a$ and $word_b$. The letters in $word_a$ can be in any order, and between $1$ and $n-1$ from $word_b$ in front and enter remaining $n-1$ to $1$ words behind. E.g. if $word_a$ was ...

0

Q: Blindfold Tic-Tac-Toe

You are playing the classic game of 3x3 Tic-Tac-Toe. You are blindfolded and you cannot see the grid, while your opponent can see it. When making a move you call out a cell. If that cell is taken you are told that it is taken and you can call out another cell until you find an empty one. You make...

strategy game

Bubbler

@Sphinx I'm inclined towards "you can't", but I don't have time to write down a full answer

Stevo

6:43 AM

hello avi :)

Avi

7:42 AM

oh, hi

Stevo

hi

lockdown finished here, so we went back to school today

Avi

2 am so I should be uh

attempting to not die from lack of sleep (aka, sleeping)

Stevo

i must say, face masks wearing for 6 hours is not good for your health

Avi

@Stevo better than uh

the alternative

Stevo

@Avi true...

Avi

7:43 AM

and actually I find that wearing a mask is relatively comfortable if you have a thinner face

Stevo

@Avi because there is air from the sides. ohh

Avi

but uh yeah

sleepy time

Stevo

ok goodbye

Avi

goodnight, and best of luck with the puzzlies

Stevo

if there is a puzzle

AncientSwordRage

8:15 AM

@Sphinx I'm over the moon about the answers

Stiv

9:54 AM

CCCC: There are fifty in America (including Louisiana and Connecticut) and one in Rome, and over time they become increasingly down-to-earth! (11)

Jafe

10:05 AM

this one's great

STA(LA+CT+I)TES, which over time become increasingly down-to-earth :)

Stiv

You got it :) I really enjoyed pulling this one together, have to say...

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