What is the difference between superposition and intersection?

[CRGreathouse]

In analytic geometry, we all know, as the slope of the line are parallel, if only a straight line, its slope is only one, so the line is parallel with himself.

Your definition is wrong.

 

[phya]

My best guess as to your meaning:

If A and B are parallel lines, and (something about a limit), then A and B are always parallel. Certainly they are always parallel, so a line is always parallel to itself, and thus a curve is also always parallel to itself.​

This isn't clear enough for me to understand. You may need to talk to a math educator (ideally, a high-school math teacher or the equivalent) who speaks your own language. He or she should be able to clear up your misconceptions.

Your reasoning is flawed, but it's hard to point out the exact flaw without a better understanding of what you're actually saying.

You had not understood that my meaning, has a chart in the appendix, in the chart has two mutually parallel straight lines, moves a straight line, in the motion process, maintains two lines parallel, until their overlapping. Therefore, the straight line own and oneself is also parallel. Similarly, the curve own and oneself is also parallel, therefore the curve is also may be each other parallel. This is my meaning.

 

[phya]

Your definition is wrong.

Why？

 

[HallsofIvy]

For exactly the reason you have been told repeatedly- two lines are parallel if and only if they never intersect. Since a line intersects itself everywhere a line is not parallel to itself. As I said before, you should have "two distinct lines have the same slope if and only if they are parallel".

 

[phya]

In the analytic geometry,
Supposition
the straight line L1 equation is y=kx,
the straight line L2 equation is y=kx+c,

then L1∥L2 is parallel,
if reduces c, then still L1∥L2.
When c=0,
L1 and L2 superposition, still L1∥L2,
if L1 and L2 not parallel, then L1 and L2 will not superpose, will intersect.
Therefore the straight line own and oneself is parallel, otherwise the straight line will not be a straight line, will intersect.
The curve is also so, the curve is also own and own parallel, therefore the curve is also may mutually parallel.
Does my this logic have what question?

 

[Mentallic]

When c=0,
L1 and L2 superposition, still L1∥L2,

You didn't even consider hallsofivy's response, you just explained it to us in a different way - which by the way, we already understand what you were trying to say. We didn't need another example to clarify it.

 

[phya]

You didn't even consider hallsofivy's response, you just explained it to us in a different way - which by the way, we already understand what you were trying to say. We didn't need another example to clarify it.

Then you whether to think the straight line own and own parallel?

 

[phya]

You didn't even consider hallsofivy's response, you just explained it to us in a different way - which by the way, we already understand what you were trying to say. We didn't need another example to clarify it.

I have not replied him? No, my new example is replying him.

 

[Mentallic]

No I don't think a line is parallel to itself because as Hallsofivy has said,

Since a line intersects itself everywhere a line is not parallel to itself.

 

[phya]

No I don't think a line is parallel to itself because as Hallsofivy has said,

Hallsofivy？

 

[phya]

No I don't think a line is parallel to itself because as Hallsofivy has said,

Your view definitely is wrong, because of you indecipherable following logic:
When c=0,
L1 and L2 superposition, still L1∥L2,
if L1 and L2 not parallel, then L1 and L2 will not superpose, will intersect.
Therefore the straight line own and oneself is parallel, otherwise the straight line will not be a straight line, will intersect.

 

[Mentallic]

Hallsofivy？

The guy that you replied to just before.

Ok then we're at a disagreement and damned if I'm the one to convince you otherwise.

When c=0,
L1 and L2 superposition, still L1∥L2,
if L1 and L2 not parallel, then L1 and L2 will not superpose, will intersect.
Therefore the straight line own and oneself is parallel, otherwise the straight line will not be a straight line, will intersect.

How can you say "therefore" when your previous line has nothing to do with the dispute. You haven't explained why or how two superimposed lines are still separate. As far as logic tells me, in 2 dimensions, two lines are parallel unless they intersect each other. Not only are two superimposed lines intersecting each other infinite times, they are now just 1 line since they are not distinct. No distinction means there is just one...

 

[phya]

The guy that you replied to just before.

Ok then we're at a disagreement and damned if I'm the one to convince you otherwise.

sorry.

 

[phya]

The guy that you replied to just before.

Ok then we're at a disagreement and damned if I'm the one to convince you otherwise.


How can you say "therefore" when your previous line has nothing to do with the dispute. You haven't explained why or how two superimposed lines are still separate. As far as logic tells me, in 2 dimensions, two lines are parallel unless they intersect each other. Not only are two superimposed lines intersecting each other infinite times, they are now just 1 line since they are not distinct. No distinction means there is just one...

Obvious:
if L1 and L2 not parallel, then L1 and L2 will not superpose, will intersect.
Because does not have not to superpose, has not intersected, Therefore the straight line own and oneself is parallel, otherwise the straight line will not be a straight line, will intersect.

 

[HallsofIvy]

You seem to be saying that a straight line "superposes" on itself rather than "intersecting" and only "intersecting" lines are not parallel. It is your distinction between "superposing" and "intersecting" that is incorrect. "Superposing" is "intersecting". A straight line is not, in the usual definition of the word, "parallel" to itself. It "lies in the same direction" as itself but that is not the same as "parallel".

 

[phya]

You seem to be saying that a straight line "superposes" on itself rather than "intersecting" and only "intersecting" lines are not parallel. It is your distinction between "superposing" and "intersecting" that is incorrect. "Superposing" is "intersecting". A straight line is not, in the usual definition of the word, "parallel" to itself. It "lies in the same direction" as itself but that is not the same as "parallel".

Superposes a straight line, with two straight line intersections, this is obviously different, the intersection is two straight line directions is different, but superposes is two straight line directions is the same. The superposition is the parallel special situation, but intersects is not parallel. This obvious different.