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Old 2020-06-23, 20:48   #54
bsquared
 
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"Ben"
Feb 2007

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Quote:
Originally Posted by xilman View Post

Here is a first take, based on what I have read so far. I am very far from infallible so my definition may be completely wrong.

Let x and y be real numbers.

BillyB(x, y) = x/y for all x, y where x and y are both non-zero.
BillyB(x,0) = 1 for all x not equal to zero.
I agree with the first but my take on his "explanation" so far is that BillyB(x,0) = x. i.e., a thing of size x cut zero times remains size x. So BillyB(0,0) = 0 by that definition.

[edit]
but that assumes some definitions... namely that x is the quantity or size of a cuttable object and y is the number of times to cut it into equal pieces. Then BillyB(x,y) = x / (y+1). Physically you can only cut something zero or more times so the domain of the function is >= 0. So, by that definition, there is no dividing by zero possible, by the everyday/ordinary definition of "divide". BillyB is not a division operation but some kind of splitting operation.

[edit-edit]
I suppose that must mean that x, y are in \script{N}^0. The guess at a definition doesn't work otherwise....

Last fiddled with by bsquared on 2020-06-23 at 21:06
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