For some reason the message below was delayed a while and thus is out of order.

Looking back, I see hh has been mentioning things like first pixel and counting 
pixels. This might be where there is confusion. I was referring to pixels by 
the LiveCode reference. 

> On Jun 14, 2019, at 4:13 PM, Dar Scott Consulting via use-livecode 
> <use-livecode@lists.runrev.com> wrote:
> 
> When we apply math, we must map what we see to our mathematical models.  What 
> we see is LiveCode.  The application of math is thus an interpretation. (The 
> interpretation of calendar year or how-old-are-you might not apply.)
> 
> I do agree with you, except for the part that one has to redefine width and 
> height. A delta does not depend on the offset.
> 
> If I create a line from 0,0 to 100,0; I get a line visible on the card, not a 
> line just off the card. The LiveCode line is between the coordinates we are 
> talking about, that is, a half pixel moved in from those, creating pixel 
> coordinates off from what we are saying.
> 
> I can get the same thing with a rectangle of rect 0, 0, 101, 1. Well, if the 
> border width is zero and the fill color is set.  This uses the coordinates we 
> are talking about. The rectangle is filled.  
> 
> The one-pixel width of the line causes it to fill that space. If there is a 
> 1-pixel square as a brush and it went from 0.5 to 100.5, it would sweep out 
> the same space as the rectangle
> 
> However, others might have a view, an interpretation, that also works. 
> 
> 
> 
>> On Jun 14, 2019, at 3:04 PM, hh via use-livecode 
>> <use-livecode@lists.runrev.com> wrote:
>> 
>> This is interestingly the same problem that made a lot of people believe
>> two thousand years were full at the end of 1999/ beginning of 2000.
>> Two thousand years were full at the END of 2000/ beginning of 2001:
>> 
>> Full year 1 has the left 0, the right 1 and the width = right-left = 1 year, 
>> ...,
>> full years 1 to 2000 have the left 0, the right 2000 and the width = 
>> right-left = 2000 years.
>> 
>>> Dar S. wrote:
>>> I like this interpretation. I don't think it is a popular view, but it 
>>> makes sense to me.
>>> I would change the range wording, though, to something like this:
>>> Pixel 0 ranges from 0 to 1.
>>> For example, the rect of a card has zeros.
>>> Maybe it depends on whether one wants to draw pixels on the intersections 
>>> of the lines
>>> on the graph paper, or in between.
>> 
>> No, this is math, not an interpretation. If you agree that counting pixels 
>> is one-based
>> then there is no pixel 0.
>> 
>> Rect (0,0,0,0) has left 0, right 0, top 0, bottom 0, width 0 and height 0, 
>> contains 0 pixels.
>> In fact it is degenerated to the point (0,0).
>> 
>> Rect (0,0,1,1) is one pixel, the first pixel on your coordinate system.
>> It has left 0, right 1, top 0, bottom 1 and width 1, height 1.
>> 
>> The width of a rect is the number of its pixel columns,
>> the height of a rect is the number of its pixel rows,
>> width*height of a rect is the number of its enclosed pixels.
>> 
>> If you wisth to count zero-based the you have to redefine width and height.
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