1. ## No Dimension

Our teacher stated that x^(0) and a point as described in plane geometry have no dimension.

He went on to say that x^(0) has no dimension because it cannot be measured.

The same applies to a point.

Why can't x^(0) be measured?

Why can't a point be measured?

2. hello my friend.
The answer to this question is something purely logic, so that you have to think and imagine to understand. The point is that the concept of "a point" doesn't really exists in gemoetry. It means that, even when you say "a point", it is not a point, it is a disc, it is a colored circle. It doesn't matter how hard you try to draw a little tiny tiny point, it's not a point again, its a circle, and since circle has two lengths, so it has two dimension, but since a real point, which doesn't exist has no dimension so it can not be measured, because it really doesn't exist, its just a logic. A line is similar to that also. A line really doesn't exist, because whatever line you draw, which is so tiny tiny and little, its again a rectangle with two dimensions. and also imagine that the points with no dimension can build a line. a line has to consist of only one dimension, but the line you draw on a paper is not a "line" really, its a rectangle with two dimension. and thats why we say that the concept of "a point" doesn't exist in reality and its a logic only, so it has no dimension and so that we can not measure it. is it clear?

3. ## ok

Originally Posted by narbe
hello my friend.
The answer to this question is something purely logic, so that you have to think and imagine to understand. The point is that the concept of "a point" doesn't really exists in gemoetry. It means that, even when you say "a point", it is not a point, it is a disc, it is a colored circle. It doesn't matter how hard you try to draw a little tiny tiny point, it's not a point again, its a circle, and since circle has two lengths, so it has two dimension, but since a real point, which doesn't exist has no dimension so it can not be measured, because it really doesn't exist, its just a logic. A line is similar to that also. A line really doesn't exist, because whatever line you draw, which is so tiny tiny and little, its again a rectangle with two dimensions. and also imagine that the points with no dimension can build a line. a line has to consist of only one dimension, but the line you draw on a paper is not a "line" really, its a rectangle with two dimension. and thats why we say that the concept of "a point" doesn't exist in reality and its a logic only, so it has no dimension and so that we can not measure it. is it clear?