Physical meaning of geometrical proposition

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A straight line in Euclidean geometry is defined as passing through an infinite number of points, but there is only one unique straight line that can connect any two distinct points. This concept is one of the fundamental axioms of Euclidean geometry, serving as a foundational principle for the discipline. The discussion highlights the challenges of accurate communication, especially for non-native speakers, in conveying complex geometric ideas. The notion that a line connects two points is a reasonable starting point for understanding geometric constructs. Overall, the discussion emphasizes the importance of clarity in mathematical communication.
Shubham Raj22
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Is it true that one straight line goes through only 2 points??
If no then how ?? If yes then why??
 
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No. A straight line goes through a lot of points. Infinitely many.
 
To add slightly to what @BvU said, it is true that there is only one straight line passing through a given pair of points. In Euclidean geometry, at least.
 
Yes, my reply was a bit corny. I understand english is not your native language and you meant something else than what the post litterally states. It shows that accurate communication isn't easy, to say the least.

In fact, this is one of the axioms (or postulates) of euclidean geometry. The first axiom, even. As such there is no proof or reason why - except that it's a reasonable thing to state. It is a starting point for a huge construct, namely geometry as we commonly know it (there are others, such as projective geometry).
 

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