Re: The logic of atheism


prabbit1@xxxxxxxxxxxxxxx wrote:

Just happened to think of something that shows how infinities don't "follow
the rules." Any infinity of order 1 (forget the proper term) is "equal in
size" to any other infinity of order 1 (so that they can be matched in a
1-to-1 manner.) I.e. the set of all whole numbers is "as large as" the set
of even whole numbers. So a square with infinitely long sides would have
infinitely long diagonals (here, diagonal will refer to any line that
crosses the side and the middle, even if it's not corner-to-corner. Don't
know if there's a more correct term than "diagonal" but it'll work for us.)
So all the diagonals would be of equal length in the segment of them that's
wholy contained in the square and and half of each diagonal woult be equal
to half of every other diagonal (since half of infinity is infinity), thus
it would satisfy the "every point on the figure [edge] is equidistant from a
central point" part of being a circle at the same time it's a square (or ANY
infinitely large 2-D, singlying connected shape, for that matter.)

Strange but apparently true (or can someone find a flaw that I overlooked
somewhere?)

You're trying to define a square which in the infinite case would
coincide with a circle. I don't know if you can do that since a square
needs four distinct vertices and lines joining them.

A better approach would be to define a different metric on the plane so
that the coordinates of the lines describing a square would be
equidistant from the center of the square.

--
Ron

.

Relevant Pages

  • Re: The logic of atheism
    ... Any infinity of order 1 is "equal in ... So a square with infinitely long sides would have ... So all the diagonals would be of equal length in the segment of them that's ... central point" part of being a circle at the same time it's a square (or ANY ...
    (talk.atheism)
  • Re: The logic of atheism
    ... Any infinity of order 1 is "equal in ... So a square with infinitely long sides would have ... So all the diagonals would be of equal length in the segment of them that's ... central point" part of being a circle at the same time it's a square (or ANY ...
    (talk.atheism)
  • Re: The logic of atheism
    ... So a square with infinitely long sides would have ... >> infinitely long diagonals (here, ... >> equal to half of every other diagonal (since half of infinity ... >> being a circle at the same time it's a square (or ANY ...
    (talk.atheism)
  • Re: Galileos Paradox
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  • Re: The logic of atheism
    ... Any infinity of order 1 is "equal in ... So a square with infinitely long sides would have ... So all the diagonals would be of equal length in the segment of them that's ... it would satisfy the "every point on the figure is equidistant from a ...
    (talk.atheism)