Well, we're talking about sub-squares, not just any old reduction. So, this
would be the reductions where both elements of the tuple are reduced by the
same scalar. But, more importantly, is the same sized square, e.g. at
{0.5,0.5}, the same square as the one at {10.5-10,10.5-10}? I think most people
would say they're different squares even if they have the same reductions
(area, circumference, etc.). So, by extension, an infinitesimal closest to zero
("iota"?) is different from one just above, say, 10 even if they're the same
size.
Along those same lines, I think an alternative answer the kid could've given
was to set the origin of the original square in the middle of the square, then
say that any square with corners at {{x,x},{-x,x},{-x,-x},{x,-x}} where x less
than ½ the length of the original square would cut into 2 squares. Where the
original answer the kid gave used an alternate definition of "square" than what
Cody was using, this uses yet *another* definition of "square", one that's more
agnostic about the space inside the square's borders. Is a square picture frame
a square? Or just a set of 4 sticks wherein the squareness property is
emergent? [pffft]
On 7/23/20 1:20 PM, Frank Wimberly wrote:
> Good point, Steve. There are infinitely many ways of resolving a vector.
> E.g. (1, 1) = (1, 0) + (0, 1/2) + (0, 1/4) + (0, 1/4) etc.
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