Mathematics

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I have one question concerning about lines in mathematics. My teacher told me that two lines of different lengths are made up of the same number of points. he told me that if we placed one above the other and join its end points and extend it they will meet at a point (for eg.) R. he told me that we can prove that by joining one point of the longer line to the shorter line and then to the point R and by continuing doing the same. If we do so we will feel that it is made up of the same number of points.
But in my view if we place one line above the other and join its end points then both the line would be slanting towards each other (because one is longer than the other). If we remove those points and the line that we joined then equals will be left because we are removing the same number of points. If we continue doing this by drawing parallel lines then both of them will meet at a point on the centre of the shorter line and if we stii continue drawing then the lines will meet at a point such that it does not lie on the shorter line. This shows that the longer line has more number of lines than the shorter one. Please clarify my doubt.
Accepted:August 31, 2010

Accepted:

August 31, 2010