Do points lie on tangent lines "only?"

[ahmet]

1 hour ago, joigus said:

peheh, pahah, poohooh.   

ahahahhaa hahaa ha aha aha 

      

hahahahha     

ok, I will try to start a new  meaningful thread.(I shall have dinner ,later..maybe)

 

 

Edited December 22, 2020 by ahmet

[CuriosOne]

On 12/21/2020 at 2:28 PM, wtf said:

I wish to refine this statement because it's a common point of confusion.

You have no proof that "At every point on the curve of the function, you can draw a tangent line, such that 1 point ( only ) is common to both," nor do you have a rigorous definition of what a tangent line is.

Rather, we have an INTUITION about what a tangent line is. In order to make the notion rigorous, we DEFINE the tangent line at a point to be the straight line passing through that point with slope equal to the derivative at that point, if the derivative exists.

That is, the the slope of the tangent line is NOT "equivalent" to the derivative; rather, it's DEFINED that way. The idea is to make precise the intuitive idea of the tangent line at a point. If you think (as students often do) that the derivative is "the same" as the slope of the tangent line, that's a misunderstanding of what's going on. There is no tangent line, formally, until we define it via the derivative.

Then (for example) we can make rigorous the intuitively clear observation that the graph of |x| has no tangent line at 0. Otherwise, we could have no proof, since without the derivative we have only an intuitive but not a rigorous notion of tangent line.

This does make my issue "more clear" as ""it is"" one point in between 2 locations, but not sure how 2 inputs for x connects the dots together "from the curve" this points "touches" on the surface of this curve..

 

""This is my idea""

It leads me to think of the logic behind calculus and ""triangles"" and the all too good pythagorean theorem, and believe it or not the ideas behind if a derivitive can be found "depending on what "point" ""the angle"" is found obviously 360, 90, 180, and 270 all =0 at least in our modern coorodinent system....

Note: I get this idea from particles in a B field, ie Alternating Currents..

[HallsofIvy]

I'm wondering if "CuriouOne"s difficulty is with the English language.  For example, in another thread (which was closed or I would responded there) "CuriosOne" repeatedly  referred to "smaller pennies" where the correct phrase would be "fewer pennies".  It is very strange that he posts questions about Calculus but makes0 basic algebra or even arithmetic mistakes.

[swansont]

25 minutes ago, HallsofIvy said:

I'm wondering if "CuriouOne"s difficulty is with the English language.  For example, in another thread (which was closed or I would responded there) "CuriosOne" repeatedly  referred to "smaller pennies" where the correct phrase would be "fewer pennies".  It is very strange that he posts questions about Calculus but makes0 basic algebra or even arithmetic mistakes.

When speaking of fractions, in the given context, “smaller” can’t be ruled out as exactly what was meant.

It’s moot, though.

[joigus]

35 minutes ago, HallsofIvy said:

I'm wondering if "CuriouOne"s difficulty is with the English language.  For example, in another thread (which was closed or I would responded there) "CuriosOne" repeatedly  referred to "smaller pennies" where the correct phrase would be "fewer pennies".  It is very strange that he posts questions about Calculus but makes0 basic algebra or even arithmetic mistakes.

I gave them the benefit of the doubt for a while, way past the reasonable... Just in case. But no. They opened another thread, and then another, and another, without ever addressing anything they were told, not even the slightest trace of a reasonable followup question. Only more questions to new, equally silly, unrelated "problems." The last thread's title was "What's 2+6?", and they said "I'm totally confused," which was the opening statement. Really? Language barrier? I don't think so.

Now, you don't have to read between the lines to know this person was pissing on all of us. Good riddance, that's all I can say.

I've seen that pattern before and I have my ideas about what can lead a person to act in that sorrily pathetic way, but I would be off base speculating about that here.

Then there are people working on social experiments out there. I just know, because I happen to know one scientist who works on that, so... You never know.

[Ghideon]

9 minutes ago, joigus said:

I don't think so.

I have to agree on that in this case; simple pictures without any written text did not seem to help them. 

 

Side note: In a general context, not regarding the issues this specific member had, I can see a point @HallsofIvy's comment: "smaller pennies" over here could be interpreted as something like "coins of smaller value" (such as  2€ vs 1€ coins). But I guess such an issue would be easy to solve if the member involved intended to have a fruitful discussion.

[joigus]

1 minute ago, Ghideon said:

Side note: In a general context, not regarding the issues this specific member had, I can see a point @HallsofIvy's comment: "smaller pennies" over here could be interpreted as something like "coins of smaller value" (such as  2€ vs 1€ coins). But I guess such an issue would be easy to solve if the member involved intended to have a fruitful discussion.

Absolutely. I don't disagree with @HallsofIvy about the specific point. What I meant, of course, was in the context of the general flow of information, which was exclusively unidirectional. I'm seasoned enough not to recognize the pattern of someone being disingenuous on purpose, just for laughs. Making fun of people whom, deep inside, you feel to be more intellectually capable than yourself, and relishing in the cheap thrill you get from pulling it off: "Look at them, they think they're so clever, and they can't tell I'm just having some fun at their expense."