Skip to main content
Mathematics

Return to Question

edited title
Link
Alex
Alex
  • 645
  • 6
  • 18

Proof: Is there a line in the xy plane that has allgoes through only rational coordinates?

added 2 characters in body
Source Link
Alex
Alex
  • 645
  • 6
  • 18

Question: Is there a line in the xyXY plane that has all rational coordinates. Prove your answer.

Idea: There is most certainly not. I believe it can be shown that between any 2 rational points that there is at least one rationalirrational coordinate. Therefore, there can not be a line that contains only rational points. The issue is that I am not sure how to show this. Any ideas? I am also open to any other ideas of how to do this. Thanks.

Note: this is for an intro to proofs study guide. So, I would prefer not to use advanced theorems.

Question: Is there a line in the xy plane that has all rational coordinates. Prove your answer.

Idea: There is most certainly not. I believe it can be shown that between any 2 rational points that there is at least one rational coordinate. Therefore, there can not be a line that contains only rational points. The issue is that I am not sure how to show this. Any ideas? I am also open to any other ideas of how to do this. Thanks.

Note: this is for an intro to proofs study guide. So, I would prefer not to use advanced theorems.

Question: Is there a line in the XY plane that has all rational coordinates. Prove your answer.

Idea: There is most certainly not. I believe it can be shown that between any 2 rational points that there is at least one irrational coordinate. Therefore, there can not be a line that contains only rational points. The issue is that I am not sure how to show this. Any ideas? I am also open to any other ideas of how to do this. Thanks.

Note: this is for an intro to proofs study guide. So, I would prefer not to use advanced theorems.

Source Link
Alex
Alex
  • 645
  • 6
  • 18

Proof: Is there a line in the xy plane that has all rational coordinates?

Question: Is there a line in the xy plane that has all rational coordinates. Prove your answer.

Idea: There is most certainly not. I believe it can be shown that between any 2 rational points that there is at least one rational coordinate. Therefore, there can not be a line that contains only rational points. The issue is that I am not sure how to show this. Any ideas? I am also open to any other ideas of how to do this. Thanks.

Note: this is for an intro to proofs study guide. So, I would prefer not to use advanced theorems.