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Topic: Matheology � 258
Replies: 53   Last Post: May 11, 2013 10:07 PM

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 dan.ms.chaos@gmail.com Posts: 409 Registered: 3/1/08
Re: Matheology § 258
Posted: May 6, 2013 6:14 PM

>The indices of the digits 1 are finite initial sequences of real
>numbers.
>Do you agree?

???

0.111
should be a valid real number .
0.11100000....
is the true form of the previous real number. That we choose not to
write the 0's is a matter of convenience.

0.11111......
should also be a valid real number .
Infinite digits ,corresponding to an infinite row, are as valid as
infinite digits of the columns .

> the idea that (even if you do not accept that reals and integers are
> in one and the same argument) the following list should not satisfy
> your symmetry expectations, should it?
>

1
2,1
3,2,1
. . . .
. . . .
you didn't even write your own example correctly (the second row is
not 2,3 )
It's transpose is as so :

1,2,3 . .
1,2 . .
1 . .
. .

Abstract?Perhaps.But just as valid .This follows from the necessity of
allowing columns to be written as rows are.
You would consider the 'stages' of writing your list as so :
1

1
2 1

1
2 1
3 2 1
-------------------
hence, the stages of writing its transpose would be

1

1 2
1

1 2 3
1 2
1

The most fitting example that I , and the fifth grader would allow ,
and you would conjure up a reason to reject would be :

1 0 1 0 1 0 . .
0 1 0 1 0 1 . .
1 0 1 0 1 0 . .
0 1 0 1 0 1 . .
1 0 1 0 1 0 . .
0 1 0 1 0 1 . .
. . . . . . . .
. . . . . . . .

Not only is it as valid as its own transpose , it is its own
transpose.And more beautiful for it.
The problem is you're not playing the same game as the rest of
us.You're playing a different game.More convoluted.And less symmetric.
The rules are never clear to anyone.
But yourself.