I am a little confused about what a single line segment of 1 unit (from say an x-y graph in an Euclidean space) would have to entail.
Let's take a line segment of 1 unit, from 0 to 1, for example. When I first thought about this, I thought that the notation [0,1] would suffice. But when I thought about 2 units, from 0 to 2, there seems to be a small inconsistency when deconstructing the two segments. The first segment would still be [0,1] (as I had already defined it that way), but the second segment would have to be (1,2]. Cleary the first unit is not the same as the second. Don't we want them both to be same?
The 1 unit segment seems to have to either include 0 or 1, but not both. So the unit would be either [0,1) or (0,1] in segment form. Or in general, for every unit to be the same, each unit would be in the form, [n,m) or (n,m]. Is this correct?
Let's take a line segment of 1 unit, from 0 to 1, for example. When I first thought about this, I thought that the notation [0,1] would suffice. But when I thought about 2 units, from 0 to 2, there seems to be a small inconsistency when deconstructing the two segments. The first segment would still be [0,1] (as I had already defined it that way), but the second segment would have to be (1,2]. Cleary the first unit is not the same as the second. Don't we want them both to be same?
The 1 unit segment seems to have to either include 0 or 1, but not both. So the unit would be either [0,1) or (0,1] in segment form. Or in general, for every unit to be the same, each unit would be in the form, [n,m) or (n,m]. Is this correct?