- Thread starter shahar
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How we define every point by unique place? How can we show that the place of the point is unique?definethe Cartesian plane, representing each point on a plane by the ordered pair (x,y) of its coordinates.

Whydo you think it can't be possible?

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A "point" and a "place" are the same thing. Where does the ordered pair come into your question?How we define every point by unique place? How can we show that the place of the point is unique?

The coordinate plane concept is based on choosing two lines in the plane (conventionally perpendicular, though that was originally not assumed), and projecting any given point onto each line. This results in two coordinates, called x and y. Clearly the ordered pair is unique; and the construction clearly can be reversed to obtain a unique point for any given ordered pair.

But again, what is the reason for your question? What observation caused you to question whether the point is unique?

All you are doing so far is asking questions, like a two-year old! They don't reveal what you are actually thinking, so I can't tell what kind of answer is needed to satisfy you.

An ordered pair of coordinates defines a unique point in a particular coordinate plane because 2 perpendicular lines have one intersection.How we define every point by unique place? How can we show that the place of the point is unique?

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Only I was thinking, that it can be proven. Why I cannot prove it?A "point" and a "place" are the same thing. Where does the ordered pair come into your question?

The coordinate plane concept is based on choosing two lines in the plane (conventionally perpendicular, though that was originally not assumed), and projecting any given point onto each line. This results in two coordinates, called x and y. Clearly the ordered pair is unique; and the construction clearly can be reversed to obtain a unique point for any given ordered pair.

But again, what is the reason for your question? What observation caused you to question whether the point is unique?

All you are doing so far is asking questions, like a two-year old! They don't reveal what you are actually thinking, so I can't tell what kind of answer is needed to satisfy you.

You can. Draw a coordinate plane. Pick any point. Its x coordinate is found by projecting the point onto the x axis. This method produces a unique result - 2 lines have one intersection. Same for y coordinate.Only I was thinking, that it can be proven. Why I cannot prove it?

Now pick any (x,y) pair. It corresponds to a unique point because again, 2 lines have one intersection.

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Only you can answer that.Only I was thinking, that it can be proven.Why I cannot prove it?

You're right that it can be, and has been, proved. You've been given two suggestions how to do so. Now you have to tell us

It could be that you are not thinking in the context of specific axioms and theorems, so you have no

In any case,

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O.K.Only you can answer that.

You're right that it can be, and has been, proved. You've been given two suggestions how to do so. Now you have to tell uswhat is lacking in you, that prevents you from carrying it out.

It could be that you are not thinking in the context of specific axioms and theorems, so you have nofoundationon which to build a proof; or it could be that you have not practiced writing proofs, so you have notoolsfor connecting the facts you know to this one. Or it may be that you don't have a specific definition of the Cartesian plane, so you don't have a cleargoaltoward which to direct a proof.

In any case,tell us what you tried, and in what way you failed to prove it.

The

The relation is ordered pairs that have a relation,

How can I use relation in Set Theory to Define that every point in the plane is unique and note by ordered pair and ordered pair is unique in the Cartesian plane?

I THINK BY DEFINITION THE RELATION I CAN PROVE IT. CAN I?

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I don't know. Can you?O.K.

TheFoundation that I find isby definition of relation R in Set Theory.

The relation is ordered pairs that have a relation,

How can I use relation in Set Theory to Define that every point in the plane is unique and note by ordered pair and ordered pair is unique in the Cartesian plane?

I THINK BY DEFINITION THE RELATION I CAN PROVE IT. CAN I?

But I don't see how what you say is relevant. What specific relation do you have in mind?

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I think about, for example,I don't know. Can you?

But I don't see how what you say is relevant. What specific relation do you have in mind?

{{1, 2}} != {{2, 1}}

If I show that set {1, 2} not equal to {2, 1} by relation of =. I can show that every point is unique?

The question is how I begin and go from point (2, 1) to set {{2, 1} and etc.

And what other relation is there between point (2, 1) to point (1, 2)?

Something like this.

You have an idea how to translate the point to set like that?...

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Are you talking about sets, or about ordered pairs? Why bring in the former? And what does your notation {{1, 2}} mean?I think about, for example,

{{1, 2}} != {{2, 1}}

If I show that set {1, 2} not equal to {2, 1} by relation of =. I can show that every point is unique?

The question is how I begin and go from point (2, 1) to set {{2, 1} and etc.

And what other relation is there between point (2, 1) to point (1, 2)?

Something like this.

You have an idea how to translate the point to set like that?...

The set {1, 2}

There is no reason to relate the pairs or points (1, 2) and (2, 1).

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To: Shahar, I think that if you would improve your understanding of English vocabulary.TheFoundation that I find isby definition of relation R in Set Theory.

The relation is ordered pairs that have a relation,

I THINK BY DEFINITION THE RELATION I CAN PROVE IT. CAN I?

Now please tell me what what textbook is

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Does that mean anything??I meant that the set that contains another set different from the set that contain the opposite set. No?