FIXED FONT

0.1-----1......1..........1.........1

0.|2....|..2......2......2......2....

0.|.3...|.3...3.......3......3.......

0.|..4..|...4....4.......4.....4.....

0.|...5.|..5........5.......5........

0.|....6|......6.......6..........6..

0.7-----7.....7...7..........7.......

0........8--8------8.........8.......

0........|9.....9..|.........9.......

0........|.1---1...|......1.....1....

0........|.|2..|...|2.........2......

0........|.|.3.|...|..3..........3...

0........|.|..4|...|.......4..4......

0........|.5---5...|...5....5........

0........|......6..|....6.......6....

0........|.......7.|......7......7...

0........|........8|...8..........8..

0........9---------9........9..9.....

4DP <=>

where w = the natural numbers

and D = the decimal digits {0..9},

AnEcAd1d2[ new & cew & d1eD & d2eD & (d1=/=d2) & (c=/=d) ]

-> L[n,n]=d1

& L[c,c]=d2

& L[n,c]=d1

& L[c,n]=d2

This is an illustration of what I call the Quad-Digit-Property, or 4DP.

It's just a typical diagonal where each diagonal digit is repeated

numerous times in that real and is part of numerous 'squares' with

corresponding diagonal digits. In fact there must be atleast 9 squares

for each diagonal digit, one for each of {0..9}.

~

WHAT IS HE TALKING ABOUT UNDIAGONALISABLE LIST?

I CAN STILL MAKE A DIAGONAL TO EVERY LIST HE MAKES!!!

Let's play a game called Cantors list. I tell you the diagonal of my

list and you tell me a real that's not on the my list. Want to play?

DIAG = 0.135791357913579...

What's your real?

YOU : 0.246802468024680..

OK, you win, that's not on my list. But this time, I'll tell you what

class of sets I'm using. All the members are fractions of ninths.

My list was actually

0.1111111..

0.3333333..

0.5555555..

0.7777777..

0.9999999..

0.1111111..

hence the diagonal was 0.1357913579...

Lets try again using only the ninths fractions.

DIAG = 0.12345671234567...

What's your real?

Rather than EXPLAIN EVERYTHING, using only a single DIAG->ANTIDIAG

function, what reals can you come up with that are not on my list?

Herc