MHB What does the following means?

  • Thread starter Thread starter cbarker1
  • Start date Start date
  • Tags Tags
    Means
AI Thread Summary
The statement suggests that in Euclidean geometry, two distinct straight lines cannot share two points without being the same line. If two lines have two points in common, they must coincide entirely. This reinforces the idea that lines can either be parallel with no points in common or intersect at exactly one point. The discussion clarifies the relationship between lines and points in geometric terms. Overall, the concept emphasizes the uniqueness of straight lines in relation to their points.
cbarker1
Gold Member
MHB
Messages
345
Reaction score
23
Dear Everybody,
What does the following means:
Two straight lines cannot have any two points of one coincide with two points of the other without the lines coinciding altogether?

I think it means that line can't overlap with itself.

Thanks,
Cbarker1
 
Mathematics news on Phys.org
I take that statement to mean that no two straight lines can have two points in common without being the same line (coinciding).
 
In other words, in Euclidean geometry, two distinct lines are either parallel, and have no points in common, or intersect, and have exactly one point in common.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Replies
2
Views
2K
Replies
9
Views
3K
Replies
2
Views
18K
Replies
10
Views
2K
Replies
72
Views
7K
Replies
12
Views
231
Replies
4
Views
2K
Back
Top