Why a line is said to have infinite number of points?

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A line is said to have an infinite number of points because there are more than any finite number of points on the line. Between any two distinct points we can find a third point between those two, so we can locate any finite number of distinct points we wish on the line. It follows that there are more than any finite number of such points, i.e. there are infinitely many points on the line.

The same is true for a circle. Any finite number of distinct points can be found on a circle.

The same is true for a line segment with distinct endpoints. It contains infinitely many points.

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Sufyan Naeem
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Updated on July 22, 2022

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  • Sufyan Naeem
    Sufyan Naeem 3 months

    Why a line is said to have infinite number of points? Is this so because a line is ever lasting or we can not count how many points does it have?

    Finite means: Having an end.

    Infinite means: No end!

    So, if the answer is the first reason viz., line is ever lasting then a closed figure like circle, ellipse etc and even a line segment must be said to has finite number of points that is, we can't count it but they have a limit or simply we can say it's indeterminate! Is that so?

    • Eff
      Eff over 7 years
      It is not the length of the line that has no end, or the length of the curve of a circle. It is the number of points that has no end.
    • Eff
      Eff over 7 years
      Then try this: there are an infinite number of points simply because here are more points than any finite number.
  • Sufyan Naeem
    Sufyan Naeem over 7 years
    Please remove your answer and if possible move it to the duplicate question of mine math.stackexchange.com/questions/590677/… I must delete this post and it needs your answer to be deleted first. Thank you!
  • hardmath
    hardmath over 7 years
    @SufyanSheikh: Duplicates are not ordinarily deleted. You might find the Meta.Math.SE post Deleting this question helpful if you wish to pursue the matter.
  • Sufyan Naeem
    Sufyan Naeem over 7 years
    what's wrong in moving your answer to the actual question. It will not violate any law of SE. It has no need here. You better move your answer to the actual post. Ittay Weiss, and 2 more users have already moved there answers to actual post. I request you to remove this!
  • Jyrki Lahtonen
    Jyrki Lahtonen over 7 years
    @SufyanSheikh: The key to avoiding downvotes is to ask better questions and/or improve the downvoted question. Pestering other users to delete their upvoted material is a bit impolite IMHO.
  • Jyrki Lahtonen
    Jyrki Lahtonen over 7 years
    @SufyanSheikh The alternative would be to merge the questions when the answers (together with their votes) will be moved as well. For that to happen the questions would need to be close to identical. Both these questions are unclear to the extent that it is difficult to rule in favor of a merger.
  • Sufyan Naeem
    Sufyan Naeem over 7 years
    @JyrkiLahtonen I know that it's hard for someone removing his/her post that has been voted. But I am asking OP to put his answer on the actual post so, I will be the first to vote his answer there. I would also improve the duplicate post of mine and give the lucid elaboration of what problem is saying. The next thing I will have to wait for the approval... Ittay wiess and 2 others have also removed their voted answers already.
  • Jyrki Lahtonen
    Jyrki Lahtonen over 7 years
    Ok. No harm asking. If hardmath feels like moving and deleting, then everything is fine. But fer crying out loud, don't flag this post asking for moderators to delete it. That's plain rude. If hardmath doesn't want to relocate his answer, you have to live with that.
  • Sufyan Naeem
    Sufyan Naeem over 7 years
    I have not asked moderators to delete the answer but only to move it @JyrkiLahtonen
  • Jyrki Lahtonen
    Jyrki Lahtonen over 7 years
    Moderators cannot move an answer by a method other than merging the questions. And I explained why merging, while an alternative, is not clear cut.