[FRIAM] square land math question

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I'm surprised EricC didn't say "it all depends on the definition of 'square'". I regard a point as a degenerate square (also a degenerate sphere, cube, etc.). It's the same sort of object as the empty set or an identity like 0 (for +) or 1 (for *).

If all we need for a square is an object with 4 sides of the same length, then a point is clearly a square and the kid is correct. But Cody's also correct. You can't divide a finite square into TWO finite squares. But you can divide it into an infinity of infinitesimal squares. And it's similarly degenerately trivial to divide a point into 2 points.

That's the beauty of math, all you need for the object is for it to satisfy its definition. All that excess meaning y'all are piling onto "square" and its vernacular referent is irrelevant. If you stopped using the word "square" and called it XYZ, then you'd be freer to see its membership.

On 7/23/20 8:40 AM, Frank Wimberly wrote:
> The point is there is no way to partition a square into two squares.
> 
> 
> On Thu, Jul 23, 2020, 9:17 AM Frank Wimberly <wimberly3 at gmail.com <mailto:wimberly3 at gmail.com>> wrote:
> 
>     Right.  When its area reaches zero it's not a square.  That is, there is only one square then.
> 
> 
>     On Thu, Jul 23, 2020, 9:10 AM Edward Angel <angel at cs.unm.edu <mailto:angel at cs.unm.edu>> wrote:
> 
>         Why would you call the limit of the increasing smaller squares a “square”? Would you still say it has a dimension of 2? It has no area and no perimeter. In fractal geometry we can create objects with only slightly different constructions that in the limit have a zero area and an infinite perimeter. 
> 

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