[FRIAM] square land math question

[uǝlƃ ↙↙↙]

Nice challenge! ... Welllll, the original question was basically how Cody might respond to the kid's suggestion that a point is a square with no area. My suggestion to Cody would be to answer the kid with a discussion about the actuality or potentiality of infinity ... or intermediately, distinguishing between *definitions* of "square".

And if you define define a square geometrically, then it makes complete sense that there is no arealess square. But there are OTHER ways to define a square. And since this kid already pulled out a sophisticated mathematical argument, it's useful and interesting to see how far that kid can go.

You're free to hem and haw about the foundations of math and which foundation you like better than another. But the point of discussing the extent of a point was to answer the kid's challenge. Answering a bright kid with "because Euclid says so" is not all that useful. >8^D

On 7/23/20 1:00 PM, Steve Smith wrote:
> Can you illuminate us as to what treating the *location* of a point as a
> *quantity* and demonstrating that the quantity can be divided
> arithmetically adds to the meaning of a point? 
> 
> While a point and a vector in R^n might be described by the same tuple,
> dividing the numeric elements of the tuple does not "partition" the
> point, it merely scales the vector which is quite useful, but I'm not
> sure if in any way doing so has any meaning that could be construed as
> having "divided" the point?
> 
> I think Euclid's geometry is pretty "standard math"?

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