Collinear Points: Are (1,0) & (0,1) Aligned?

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Discussion Overview

The discussion revolves around the collinearity of the points (1,0) and (0,1). Participants explore the definitions of collinearity and lines, questioning the clarity of the original question and the implications of defining these terms.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants question whether the original inquiry is specifically about the collinearity of the two points with each other or if it pertains to a broader context.
  • There is a discussion about the definition of a line, with some asserting that a line is defined by two points, which leads to the conclusion that the points (1,0) and (0,1) are trivially collinear.
  • Others argue that to discuss collinearity meaningfully, one must first clarify what is meant by a line, suggesting that definitions are intertwined.
  • Several participants express the need for a clear definition of a line before addressing the question of collinearity.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions of collinearity and lines, leading to multiple competing views on how to approach the original question.

Contextual Notes

The discussion highlights limitations in definitions and assumptions regarding collinearity and lines, which remain unresolved.

Zubair Ahmad
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Are the points (1,0) and (0,1) collinear?
 
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Zubair Ahmad said:
Are the points (1,0) and (0,1) collinear?
What is a line to you?
 
Are you asking if (1,0) and (0,1) are collinear with each other ? - or did you intend to ask a different question?
 
fresh_42 said:
What is a line to you?
Combination of collinear points
 
Stephen Tashi said:
Are you asking if (1,0) and (0,1) are collinear with each other ? - or did you intend to ask a different question?
Same as you understood
 
Zubair Ahmad said:
Combination of collinear points
To say what colinear is, you first have to say what linear is, in this case a line. You cannot define colinear by line and line by colinear at the same time. In this case they would be equivalent and the answer would be trivially yes. So in order to get some meaning to the question, you have to put some truth in it somewhere. That's why I asked, what a line is to you. How can I answer a question about colinear points, if it isn't clear what a line is?
 
Ok what is a line then
 
Zubair Ahmad said:
Ok what is a line then

I think you need to answer this first before @fresh_42 can answer your posted question.
 
Two points define a straight line. So the original question is trivially answered by yes. Usually when asking about collinear, the question involves more than two points.
 

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