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Talking about true and false

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KerimF

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Hi All,

Is the following definition true or false?

Two straight lines are said parallel if they don’t intersect.

Kerim

Warning: :twisted:
The object of this thread is rather philosophical on human nature and logic :grin:
Therefore the following posts and possible discussions will be more interesting to philosophers :wink:
 

Logically its True

Oh... I didn't expect this answer :wink:

I mean... are you sure it is true :smile:


Added:
And this topic will be better appreciated by scientific persons... starting from the undergraduate students.
 
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Are you kidding? :grin:

Please read the definition very carefully ;-)

And this is just the first step... :twisted:
 

Hi Alex, and in your opinion... is it true or false now ... in our days :)

As you know... if it is true one cannot prove, it is wrong.
 

Are there really only these two options: True or false? Nothing "in between"?
LvW
 

Okay... Let us see it from another angle.

I think we agree on how two parallel straights should look like... right?
Now... can we found two straights that are not parallel and satisfy the above definition?
If we can (of course we can) this means that the definition is not fully true since it doesn't apply on true parallel straights ONLY.

Kerim

Note: This is just the beginning :)
 

"Another way to describe the differences between these geometries is to consider two straight lines indefinitely extended in a two-dimensional plane that are both perpendicular to a third line:

* In Euclidean geometry the lines remain at a constant distance from each other even if extended to infinity, and are known as parallels.
* In hyperbolic geometry they "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultraparallels.
* In elliptic geometry the lines "curve toward" each other and eventually intersect.

Non-euclidean geometry can be understood by picturing the drawing of geometric figures on curved surfaces, for example, the surface of a sphere or the inside surface of a bowl."

Non-Euclidean geometry - Wikipedia, the free encyclopedia

I can't imagine a between state.

Alex
 

I can't imagine a between state.


Alex - Ok, perhaps it is better to replace "in between?" by "it depends"?
(By the way: There are many things I can't imagine, but they seem to be true, anyway.)

Kerim, I think you have forgotten to specify: "In a two-dimensional space"?

LvW
 

Hi Alex,

Are we talking about the same subject?

On your side, you present how parallelism is defined by different geometries and, there is nothing wrong in what you said.

On my side, I just wrote the definition:

Two straight lines are said parallel if they don’t intersect.

which is clearly different from the known three definitions and I asked if it is true or not.
I was expecting that ALL readers here will agree (in this first stage) that ‘it is wrong’, because two non coplanar straights don't intersect and are not parallel. Hope you got my point now :smile:

Kerim
 

Now, since this problem has been solved I again like to ask "true or false" ?

My question brings us back to electronics:

Assume an operational amplifier (VCVS) with a constant gain of 1E4 (all other parameters ideal) with a feedback path that is connected to the non-inverting input. The positive feedback factor is 0.1 [1k/(1k+9k)]. The device is powered with+-15 volts and the input signal is connected to the inverting terminal.
Question: Formal application of Blacks gain formula gives a gain of Vin/Vout=10.01.
True or false?

(By the way: A circuit simulation program gives the same result)
 

I think he did it on purpose...:smile:
Alex

You are right Alex...

In fact this is the first definition I was taught when I was a little kid at school (I think it is the same everywhere). All students and I in my class didn’t complain. At this age, the universe we perceive in geometry was rather planar and we were glad to draw straight lines that don’t intersect and say... Hey here are more parallel lines :grin:

Now after I knew that the first definition I heard of is wrong...

(1)
Should I deduce my teachers were ignorant or liars?
Of course not, because if I would teach basic geometry to little kids now I will start with this wrong definition because it represents the right first step for them to learn geometry.

(2)
On the other hand, I can’t deny that this wrong definition was the base of my actual right knowledge.
So, should I keep this definition in my mind as a scientific truth or just as a souvenir?
To me in least, it is a mere souvenir to remind me the simple mind I had when I was a kid :oops:

To be continued to the next stage... unless someone doesn’t agree that the definition of interest is wrong :roll:


Note:
As I said earlier, the object of this logical discussion will lead us to a great and obvious conclusion that contradicts the belief of billions on earth mainly their scholars. That is why I wish that every reader who contributes to the discussion be based on his own logic and point out anything that doesn’t look right to him.

---------- Post added at 12:01 ---------- Previous post was at 11:30 ----------

...the input signal is connected to the inverting terminal.

Charming... I mean... the connection of a voltage source directly to the inverting input of an opamp...
Unless 'input signal' means a current source :roll:
 
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Unless 'input signal' means a current source

A current source at the input of a VCVS? This was not my intention.
LvW
 

Referring to the initial theorem, the "trick" is to omit it's implicite relation to planar geometry. In school, it's exclusively used in this context. It can be however extended to 3D geometry by using planes instead of lines.

Considering the fact, that it's a well founded theorem in a specific field of mathematics, the answer to the original question should be probably be: It's true, but incomplete.
 

Kerim, back to your original question:
Two straight lines are said parallel if they don’t intersect.

I think, one could even discuss the question if "lines" exist resp. are defined only in planar geometry (and not at all in a 3-dimensinal space?).
(wikipedia definition: "an infinitely-extending one-dimensional figure that has no curvature")
 

In a euclidean 3 dimensional space, you can have one line above another - they can be at right angles to each other or any angle (0-360 deg) - they don't intersect if the planes they lie in are parallel, only one special case is parallel lines.
In curved space the same is true - it's just that the planes & lines are not "straight" to a global observer - but they are as good as straight to a local observer.
Regards, Orson Cart.
 

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