Neighbor says: >I should have used "disjoint" rather than "taken separately".
Good. So If the two lines (the "bisects"?) are disjoint, then you have either of the following two cases:
1. The intersection point is left behind, neither of the two bisects has it as a member. Therefore the original line hasn't been bisected, its been trisection into two lines plus one lone point. If you try to put the two lines back together without that third component, you don't get back the original line, you get a line with a single point missing...
2. The intersection point goes with one of the lines but not the other. They are not symmetrical, not equal in every way (though they could be equal in length,) they are not equal in other properties.
Neighbor says: >A line has length,which we can notice, but a point is dimensionless, without both length and width, so we can't see a point , therefore I'm disposed to use the term "imagine" for a point.
You couldn't see an infinitely thin line with your eyes any more than you could a point. With you mind you can see both.