The Foundation of the "degree" as relation of Geometric Form

What is the basis for reason? And mathematics?

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by -1- » Thu Aug 09, 2018 1:17 pm

wtf wrote:
Wed Aug 08, 2018 10:20 pm
-1- wrote:
Wed Aug 08, 2018 10:04 pm
I have seen people melt down on forums before because they backed the wrong horse, so to speak, and they got so emotionally entangled in their own confusion that they temporarily lost their mind.
Project much?

Just answer my question. What's the distance on the Euclidean plane between the origin and (1,1)?

Also read this. https://en.wikipedia.org/wiki/Metric_space

Length is a nonnegative real number. If you don't know that you need to remedy your ignorance.
A Euclidean plane is not measuring REAL distances. It is a conceptual plane. The answer to your question is square root of two in units of unit length.

You still haven't answered my questions though. This is it, a bit paraphrased (although your answer to my original question will be accepted too, if acceptable):

How much is sin(1Radian)? How much is tan(2Radian)? sin stand for sinus function, tan stands for tangent function.

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by wtf » Fri Aug 10, 2018 6:19 am

-1- wrote:
Thu Aug 09, 2018 1:17 pm
A Euclidean plane is not measuring REAL distances. It is a conceptual plane. The answer to your question is square root of two in units of unit length.

You still haven't answered my questions though. This is it, a bit paraphrased (although your answer to my original question will be accepted too, if acceptable):

How much is sin(1Radian)? How much is tan(2Radian)? sin stand for sinus function, tan stands for tangent function.
Units of unit length. Intellectually unserious much? It's sqrt(2). A member of the set of real numbers. That's because:

* In high school they taught you the Euclidean distance formula d = sqrt(x^2 + y^2). I doubt you raised your unserious and sophistic objections about units at that time.

* In real analysis they define the abstract idea of length as a metric, a function from pairs of elements of some space, to the nonnegative real numbers. A distance is defined as a real number.

* Going on a little higher on the math tree, they generalize the idea of length and volume of line segments and cubes to arbitrary sets of real numbers. This is called measure theory. A measure is a function that assigns to as many subsets as possible of some given set, a nonnegative real number. And let me add that measure theory is one of the fundamental building blocks of the theory of Hilbert spaces, which is the setting for quantum mechanics. So n advanced mathematical physicist would understand exactly what I'm saying. Measures are numbers. Integrals in QM are numbers. Pure, unitless numbers.

That's math. That's how it is. And I hope I just showed you that even in advanced parts of physics, that's also how it is.

Now when we APPLY math of course there are units. A set theorist can define the abstract number 3, and Farmer Brown might have 3 cows. Theory and application. It's 400 miles from city X to city Y. Nobody's denying that.

But in the underlying theory, distances are real numbers.

Now if we were trying to define gravity, physics would take priority over math, because math doesn't know anything about gravity. But when it comes to fundamental mathematical abstractions like length and angle, it's the mathematical definition that is deeper than the physics one.

It's perfectly clear to me that any mathematical physicist -- that is, someone trained to both disciplines -- would understand this. If you ever looked at QM, it's just basic functional analysis. It's abstract math based on metric spaces and measure theory. Distances are nonnegative real numbers, it's baked into QM from the bottom up.

Now I have written you a nice serious response. Personally if you respond I'd prefer substantive engagement with what I wrote, not unserious games like "units of unit length." There is no "unit length" in the international Meter-Kilogram-Second standard. Your argument depends on the concept of physical measurement as inherently being associated with a physically meaningful unit. The sqrt(2) example shows that pure distance is a real number; and APPLICATIONS of distances have units. The pure abstraction of of sqrt(2) is deeper than physics. Old Pythagoras knew that. He said All is Number. He had your weak argument in mind when he said it.

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by -1- » Fri Aug 10, 2018 2:51 pm

WTF, you still haven't answered MY question.

What is the value of sin (2Radians) and what is the value of tan(1radian)?

It's the third time I ask these, why can't you heed to my request, when I heeded to yours?

Now let me ask you a different question as well. In Euclidean space, what is the area bounded by segments (0,0), (0,2); (0,2) (2,2); (2,2), (2,0); and (2,0) (0,0)? Please reply with your answer. I hope you got 4.

Now consider this: what is the length of the segment between (0,0) and (0,4)? I hope your answer is 4.

Now consider this: are the two 4-s equivalent? I hope your answer is "no".

You must translate this conceptual difference to your ill-gotten (sorry) idea that "all in Euclicean space is numbers." No. That is not correct. If that were correct, then the two 4-s above would be equivalent to each other.

But you agree (I hope) that the two fours denote different DIMENSIONALITY.

And this is where you got confused. You took sheer numbers and you dropped their dimensionality.

Hence, if you wake up and answer my question, you will notice that sin(2radian) exists, and tan(1 radian) exists. This could not happen if radian was not an angle.

In fact, in pure math (which you seem to have appropriated ownership of), people often write sin (pi), or tan(2pi) and so on.

These are numbers of which you take the sinus value of. But the numbers are ANGULAR DIMENSIONS. Much like a square of sides equal to 2 unit lengths are four, but they are AREAL DIMENSIONS, whereas a line segment of 4 unit length is a four, they are in LENGTH DIMENSION (1 D).

This "dropping of the units in applications" to reduce the values to numbers of no dimensions units (such as meters, square meters, radians, degrees, etc.) is what confused you. You took the dropped dimensions, and declared that the resultant is just a number. But IT IS NOT JUST A NUMBER, it still carries dimensionality with it.

Much like in the above example 4 is not the same as the other 4. You can't disregard dimensionality even if dimensionality is not expressly expressed. But YOU do. And that is the way of your erring.

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by Eodnhoj7 » Fri Aug 10, 2018 5:34 pm

-1- wrote:
Fri Aug 10, 2018 2:51 pm
WTF, you still haven't answered MY question.

What is the value of sin (2Radians) and what is the value of tan(1radian)?

It's the third time I ask these, why can't you heed to my request, when I heeded to yours?

Now let me ask you a different question as well. In Euclidean space, what is the area bounded by segments (0,0), (0,2); (0,2) (2,2); (2,2), (2,0); and (2,0) (0,0)? Please reply with your answer. I hope you got 4.

Now consider this: what is the length of the segment between (0,0) and (0,4)? I hope your answer is 4.

Now consider this: are the two 4-s equivalent? I hope your answer is "no".

You must translate this conceptual difference to your ill-gotten (sorry) idea that "all in Euclicean space is numbers." No. That is not correct. If that were correct, then the two 4-s above would be equivalent to each other.

But you agree (I hope) that the two fours denote different DIMENSIONALITY.

And this is where you got confused. You took sheer numbers and you dropped their dimensionality.

Hence, if you wake up and answer my question, you will notice that sin(2radian) exists, and tan(1 radian) exists. This could not happen if radian was not an angle.

In fact, in pure math (which you seem to have appropriated ownership of), people often write sin (pi), or tan(2pi) and so on.

These are numbers of which you take the sinus value of. But the numbers are ANGULAR DIMENSIONS. Much like a square of sides equal to 2 unit lengths are four, but they are AREAL DIMENSIONS, whereas a line segment of 4 unit length is a four, they are in LENGTH DIMENSION (1 D).

This "dropping of the units in applications" to reduce the values to numbers of no dimensions units (such as meters, square meters, radians, degrees, etc.) is what confused you. You took the dropped dimensions, and declared that the resultant is just a number. But IT IS NOT JUST A NUMBER, it still carries dimensionality with it.

Much like in the above example 4 is not the same as the other 4. You can't disregard dimensionality even if dimensionality is not expressly expressed. But YOU do. And that is the way of your erring.
In agreement with "1"...holy shit what is the world coming too?

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by wtf » Sat Aug 11, 2018 2:38 am

-1- wrote:
Fri Aug 10, 2018 2:51 pm
WTF, you still haven't answered MY question.
@-1- You raised a number of actually good points. I do have responses which I'll post later.

By the way are you asking me for the sin of 2 radians? Or 2 pi radians? I confess I don't understand the point of the question either way but I just want to be sure. Once you clarify I'll respond. But I do admit I have no idea how that fits into our discussion. The sin is the sin. It's a function that inputs a real number and outputs a real number in the range [0,1]. Or it inputs a complex number and outputs a complex number.

Ok anyway I'll write more later. I thought your point about the square and the line segment was the most interesting thing you've said so far. I do have a response but it will take me a while to write up, it's kind of involved in my mind. But bottom line, is it the same 4? Yes.

There is only one 4 in the Platonic world of abstractions, namely the thing pointed to by all the expressions

- '4',
- '2+2',
- '3.999...",
- "the smallest n for which there are at least two distinct nonisomorphic groups of order n",
- etc.

All those various representations we humans could ever write down, all "point to" the abstract, Platonic ideal of the number 4.

And if you're not a Platonist but rather believe that the objects of mathematics have existence only insofar as the symbols talk about them, even then there is a unique set of real numbers; and a unique number 4. In other worlds whatever your philosophy of math, there is only one real number 4, which can be used a lot of different ways.

It can be used as an age, like a 4 year old kid. It can be an area, Farmer Brown's 4 acres and 3 cows. It can be a length, the Euclidean distance between x = 3 and x = 7 on the real line. Or a fancier way to say the same thing, it's the Lebesgue measure of the interval [0,4]. And yes it is ALSO the Lebesgue measure of the square you described!

You gotta get this! The number 4 is the number 4. What people USE it for is something else. And yes very much more on point, the 4 that represents an area in the plane is the same exactly 4 as the 4 that represents the length of a line segment. This is how mathematicians regard your question. It's the same 4. You do not have to LIKE that fact, but I am simply describing how math works. The length of a line is defined as a real number; and the area of a square is defined as a real number. There is only one real number 4. There aren't two of them.

When a botanist sees the number 4, it's the petals on a flower. When a biologist sees 4, it's 4 bacteria or 4 elephants. A chemist has 4 electron shells. A classical physicist has 4 feet times 100 pounds = 400 foot-pounds of work done. A quantum physicist has 4 as some amplitude.

But a mathematician studies the number 4 itself. The pure Platonic ideal of the number 4.

Even if you don't have an affinity or an interest for mathematical abstraction; at least you can agree that mathematicians have such an affinity!

Well anyway that's not a bad response considering I was only posting to say I'll respond better later! But yes, numbers in math are pure. If you want to say, "Oh, well, physics is all that matters and math is bullshit," ok, take that position and go in peace.

But if the reductio to absurdity of that position does gnaw on your conscience a bit, just remember that science is about the world, and math is about abstractions. The fact that many practical people have a use for the number 4 is of no interest to the mathematician. The mathematician studies the number 4.

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by -1- » Sat Aug 11, 2018 3:29 pm

wtf, you failed to show how 4 and 4 are different yet the same.

In Euclidean space 4 can be a length of four, or an area of 4.

Once you subtract the information of whether it's length or area, the number is the same. Yet if you are talking analytic geometry, it is substantially different whether 4 is a length or an area.

You must show how AFTER the subtraction of the dimensionality, the mathematician as you are, can still decipher the difference. I challenge you to admit that that is impossible.

I shall show it to you this way:

A number of areas, lengths, and angles have been established in Euclidean space. After their numerical value was found, the dimensionality was subtracted (taken out of the knowledge base). The numbers thus derived are:

2, 65, 33923, 29, 393, and 291.

Please tell me which numbers were measured as length, which as areas and which as radians.

I hope you admit this is impossible.

Yet the numbers with the information of dimensionality attached to them were numbers, yet, they denoted different measures.

This is the point I am making. The point is that numbers by themselves are not indicative of qualities and quantities in Euclidean space and in analytic geometry. Their dimensionality is just as important as the number that denotes the quantity of that dimensionality. Furthermore, dimensionalities are not interchangeable. Furthermore, and therefore, dimensionalities are not negligible, even if they are understood without being expressed in units as in Euclimedan geometry.

Dimensionalities are exact, precise, necessary to be stated (or understood), non-interchangeable and not negligible even if they are not expressly stated.

RADIANS are ANGLES. LENGTH is LENGTH. AREA is AREA.
Last edited by -1- on Sat Aug 11, 2018 3:48 pm, edited 3 times in total.

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by -1- » Sat Aug 11, 2018 3:35 pm

wtf wrote:
Sat Aug 11, 2018 2:38 am
By the way are you asking me for the sin of 2 radians? Or 2 pi radians? I confess I don't understand the point of the question either way but I just want to be sure. Once you clarify I'll respond.
What is the value (to as many decimal places as you wish) of sin(1radian)? What is the value of tan (2Radians)?

Please notice the absence of pi.

For the record, the pi was absent in the previous three times I asked the same question. I needed to ask the SAME question four times before your answer, and three times before you would respond to just even acknowledge I asked a question.

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by wtf » Sat Aug 11, 2018 10:04 pm

-1- wrote:
Sat Aug 11, 2018 3:35 pm

What is the value (to as many decimal places as you wish) of sin(1radian)? What is the value of tan (2Radians)?
I'd write them as sin(1) and sin(2), respectively. They're irrational numbers so that their complete decimal representation can't be written down. That's a defect in decimal expressions, not in the real numbers themselves (which are logically prior to decimal representations). But note that both sin(1) and sin(2) are nevertheless finitely describable, in fact as sin(1) and sin(2) as you can plainly see. Of course I owe you a proof that the sin function can be finitely described, but that's not hard. The sin is defined as its Taylor series about 0 that you learned in freshman calculus. The summation symbol expression for that series consists of a finite number of characters. So sin(1) is as complete and perfect expression of that particular real number as its "infinite" decimal expression is.

sin(1) can be written out in a finite number of characters using a summation symbol. That expression could be programmed on a Turing machine or a modern programming language and executed on your laptop. It would approximate sin(1) to any desired degree of accuracy given sufficient computing resources. In short, sin(1) is a computable number. It inherently bears only a finite amount of information, not an infinite amount as you apparently mistakenly believe.

Moral of the story: Don't confuse a real number with any of its representations.

https://en.wikipedia.org/wiki/Computable_number


-1- wrote:
Sat Aug 11, 2018 3:35 pm
Please notice the absence of pi.
Ok. But you're not making any sensible point. There's no difference. You are not making any technical or philosophical point. You are merely demonstrating that you didn't take real analysis and don't know what a real number is. That's perfectly cool, a lot of people don't take that class, it's just for math majors. But now that I've explained this to you, you are no longer ignorant of the math and I urge you to try to think this through in a way that's intellectually honest.
-1- wrote:
Sat Aug 11, 2018 3:35 pm
For the record, the pi was absent in the previous three times I asked the same question.
I think I understand why I didn't read your question earlier. Most of your previous posts began or contained gratuitous insults and personal comments. I didn't read anything you wrote.

It's really not till your example of the same '4' being used to describe the area of a square and the length of a line segment that I took you seriously at all. Your first half dozen posts to me were f-bombs and insults. I commend you for finally making an active choice to engage in productive dialog like an adult. That still doesn't oblige me to go back and read your earlier shit.

But more to the point, whether pi is there or not makes no difference. You think you're making some kind of point but you're only showing you have no idea how the real numbers work. There's no difference between sin(1) and sin(pi) except that the later is an integer and sin(1) is irrational. But so what? The fact that you think this makes a difference, tells me how much you know. So you are going to have to come to me on this issue because the entire premise of your question is wrong.

Why don't you tell me what YOU think the difference is.
-1- wrote:
Sat Aug 11, 2018 3:35 pm

I needed to ask the SAME question four times before your answer,
You were an obnoxious jerk earlier, and ignorant of mathematics. Now you're only ignorant of mathematics. I'll always engage seriously with someone who wants to understand how mathematicians see things. I rarely waste time with f-bombers and insult throwers. Once again I do mean to emphasize that I APPRECIATE that you stopped doing that. But that does NOT obligate me to go back and read your earlier posts.
-1- wrote:
Sat Aug 11, 2018 3:35 pm
and three times before you would respond to just even acknowledge I asked a question.
When you said something interesting (area versus length in the Euclidean plane) I read your post in detail and responded intelligently. The other posts I didn't read. Surely you can understand this point. I take as proof the very fact that you've started being interesting instead of obnoxious. So you yourself at some point decided to try to be understood rather than to just hurl poo. Why are you acting peeved that I didn't take you seriously during your poo-throwing phase?

By the way, forget all this shit. This is a stupid conversation. I am much more interested to know what you think about my comments that the Lebesgue measure of a square or a line segment are both the SAME number 4. Did you find this interesting? Do you believe it? How does it affect your overall thesis that units are inherently part of numbers? It's interesting that you pointedly IGNORED EVERYTHING I SAID THAT REFUTED YOUR THESIS to go off in some lame direction about sin(1). And not even TALKING about sin(1), but only whining about being ignored. What is your fucking point about sin(1)?

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by -1- » Sat Aug 11, 2018 10:46 pm

wtf wrote:
Sat Aug 11, 2018 10:04 pm
-1- wrote:
Sat Aug 11, 2018 3:35 pm

What is the value (to as many decimal places as you wish) of sin(1radian)? What is the value of tan (2Radians)?
I'd write them as sin(1) and sin(2), respectively. It's interesting that you pointedly IGNORED EVERYTHING I SAID THAT REFUTED YOUR THESIS to go off in some lame direction about sin(1). What is your fucking point about sin(1)?
Everything you said did not refute my point at all. All you do is substitute sheer numbers without their dimensionality, while ASSUMING their dimensionality. My task is to point out to you that you take dimensionality into consideration, and can't apply your math to them without assuming or understanding even if not stated, their dimensionality.

One way of pointing out this was back two posts ago, where I suggested this:
-1- wrote:"A number of areas, lengths, and angles have been established in Euclidean space. After their numerical value was found, the dimensionality was subtracted (taken out of the knowledge base). The numbers thus derived are:

2, 65, 33923, 29, 393, and 291.

Please tell me which numbers were measured as length, which as areas and which as radians."
Of course you could not. This established, and I tried to show it to you, the importance of dimensionality. A number can represent any of those values, but without dimensionality, you don't know which is which. And yet they do happen in Euclidean space.

You referred to this as something valid, or interesting, or a having a point. You did not say anything more about it. I am curious what you could say to that. Remember, the point is that without any information leading to the dimensionality of a number, it is not a representative of a quantity in Euclidean space.

Now the same thing is going to happen, in a slightly different way.

This is why I needed you to acknowledge that sin(1radian) and tan (2 radians) exist. You wrote them as sin (1) and tan(2) but you acknowledged that they are radians, and your way of writing them is a shortcut, perhaps, if you want to call it that. You do agree that we are talking radians when you take sinus and tangent functions of radians.

You can only take the sinus function and the tangent function of ANGLES. This is an irrefutable fact of math.

Could you take the sin and/or tan function of metres? Seconds? Coulumbs? no you could not. You can only take the sin function of an ANGLE.

Here is the point. Do I need to spell it out for you? You are living in a world where short forms are rampant. But short forms do lose an important piece of information. Those who are familiar with the subject matter, and are in the practice of understanding short forms, will read the notations perfectly well: sin(1) and tan(2). But they will understand that 1 and 2, respectively, in the brackets, are angles expresed in Radians. Because a sinus function is only meaningful if applied to an angle.

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by -1- » Sat Aug 11, 2018 10:57 pm

wtf wrote:
Sat Aug 11, 2018 10:04 pm
By the way, forget all this shit. This is a stupid conversation.
Forgetting all this shit (the notion that dimensionality of Euclidean space is important and necessary to take into consideration in understanding and applying analytical geometry; and ultimately, that radians are angles, not length; and that you initially insisted that radians are length, whereas I insisted, and still do, that radians are a measure of angle, despite being defined by a length) would be very convenient to you at this point. I admit that is true.

This is only a stupid conversation because you insist on a false fact. That false fact being that radians are a measure of length. You are trying to find holes in my logic, and are looking for it in all the wrong places. Don't expect an intelligent conversation when one party insist that the truth is shit and stupid.

You did admit that you can take the sinus function and the tangent function of radians. Yet you must also admit that sinus and tangent can only be taken of angles. Therefore, necessarily the radians are a measure of angle. Yet you insist (at least you have not refuted your insistence yet) on the issue of radians being a measure of length. You mistakenly equated radians to length, because a length was used in the definition of a radian measure of angle.

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by wtf » Sat Aug 11, 2018 11:05 pm

-1- wrote:
Sat Aug 11, 2018 10:57 pm
Yet you must also admit that sinus and tangent can only be taken of angles.
Oh I see your mistaken point.

No, sin is best understood as a map from the complex numbers to themselves defined by an infinite series. It inputs a complex number and outputs a complex number. If you restrict it to the reals, it inputs a real number and outputs a real number in the closed unit interval.

There's no point to going on with this conversation if all you're going to do is keep noting that definitions in physics can be different from definitions in math, and then saying that I'm wrong because I'm trying to explain the math. We were at this point a couple of posts ago. If your point is "Math sucks and physics rules," ok you expressed yourself and we're done.

You have to at some point say, "OK I get it, in math the sin is a function of a real or complex variable." You can't say that's not true simply because they taught you something different in physics class. I'm telling you what the sin function is. But you know what? EVEN IN HIGH SCHOOL they told you that, because when they showed you how to GRAPH the sin function they put the ENTIRE REAL LINE on the x-axis and showed the wavy up and down sin function. Those were the REAL NUMBERS on the x-axis. And yes at that time in you mathematical education they told you the sin is defined in terms of "angles," but that's a bit of a lie because they didn't really give a rigorous definition of an angle. In higher math the sin function is a particular convergent infinite series defined on the complex numbers. That is how it is.

Now if your response is, "Oh yeah well physics says blah blah," or "My high school teacher said blah blah, " that is not helpful. If you don't like what I'm telling you then either you simply are saying "Fuck math," which is fine with me if you do; or you're saying you don't BELIEVE me about the math. If the former, we're done. If the latter, I'll be happy to provide the references.

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by wtf » Sat Aug 11, 2018 11:21 pm

-1- wrote:
Sat Aug 11, 2018 10:46 pm

You can only take the sinus function and the tangent function of ANGLES. This is an irrefutable fact of math.
That's not a fact of math. That's a fact of your limited knowledge of math. It's a function of the level at which your math education ended. The sine function is defined in terms of the complex exponential. It's a function of complex numbers. You're confusing your own limited education in math, with math itself. You are holding to the thesis that any math you don't happen to know, doesn't exist. That's not a good position to take for someone who doesn't know that sin is a function at the very least of a real number, and makes the most sense when understood as a particular function a complex number.

Math goes way beyond SOHCAHTOA. I hope you're not going through life insisting that everything is exactly the way you learned it in high school.

But then again ... don't you remember when they taught you how to graph the sine function? They put the entire set of real numbers on the x axis. Your high school brain said, "Oh those are angles there because teacher says so." I hope with your adult brain you can look back and say ... Oh those are REAL NUMBERS there. The sine function inputs a real number! Aha!! I see what wtf is saying.

You know there are a lot of things in math that are taught one way at a given educational level, and are taught a very different way at a more sophisticated level. We don't teach the Peano axioms to grade schoolers when we're teaching them to count 1, 2, 3, 4, ... That doesn't justify a kid becoming an adult and denying that the Peano axioms are valid because he didn't hear about them when he was four years old. Same with your concept of the sine function and of numbers in general, especially the real numbers. You can't just say, "I was taught what I was taught and I'm not going to listen to anything else."

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by wtf » Sun Aug 12, 2018 12:26 am

ps -- I'm writing this as a separate post because I want to call attention to it in isolation.

In your point (which I still don't get) about sin(1), you are trying to make the point that sin is a function of an angle. But you are acting like sin(1) is not defined while sin(pi) is. But 1 is indeed the radian measure of an angle. Every real number is the radian measure of some angle. There isn't any difference in quality or meaning between sin(1) and sin(pi). The fact that you think there is, indicates a profound misunderstanding of something on your part. I'm not sure exactly what.

Do you understand that 1 is a real number; and that 1 radian is indeed the measure of an angle? After all there are 2pi radians in a circle, so an angle of 1 radian is 1/2pi or a little less than 1/6 of a circle. Don't you get that?

I truly and honestly do not understand your point about sin(1). It makes no sense. It doesn't show anything at all. 1 is a real number so it's a valid input to the sine function. Or if you prefer, an angle of 1 radian is a perfectly valid angle, and it's an input to the sine function. So if you want to say the sine function inputs angles I have no disagreement, but you are still not making any sensible point.

Again: If I agree with you for sake of discussion that the sine function inputs angles, that doesn't change anything. It doesn't support your point or invalidate anything I've said. So I really don't get your point about sin(1).

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by -1- » Sun Aug 12, 2018 2:29 am

wtf wrote:
Sun Aug 12, 2018 12:26 am
But you are acting like sin(1) is not defined while sin(pi) is.
Where do you get this nonsense?

Where did I act as if I believed sin(1radian) is not defined whereas sin (pi radian) is?

In no point in the conversation did I insinuate that sin(1 radian) is undefined. While you may have interpreted it that way, that's your perception.

The rest of your treatise in the post that stated your doubt if I believed sin(1 radian) is undefined therefore is moot.

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Re: The Foundation of the "degree" as relation of Geometric Form

Post by -1- » Sun Aug 12, 2018 2:37 am

wtf wrote:
Sat Aug 11, 2018 11:21 pm
-1- wrote:
Sat Aug 11, 2018 10:46 pm

You can only take the sinus function and the tangent function of ANGLES. This is an irrefutable fact of math.
That's not a fact of math. That's a fact of your limited knowledge of math. It's a function of the level at which your math education ended. The sine function is defined in terms of the complex exponential. It's a function of complex numbers.
You are lost in the forest for seeing neither the trees nor the forest, my friend, WTF.

The sin function's VALUES are CALCULATED with the utilization of complex exponential functions.

The Sin function is DEFINED otherwise. It is defined as the farther side of a right-angle triangle devided by the longest side of a right-sided triangle. This is the DEFINITION. The values of it are calculated differently. Please forgive me that I did not use the proper and correct terms for the angle, the farthest side and for the longest side. I trust you can conceptualize my description this way.

There exist a sin definition only for ANGLES. Show me any, and I mean any, definition (DEFINITION, not numeric evaluative process) of any other dimensionality that can be taken the sinus function of: metres, seconds, weight, force, whatever.

Again, you demonstrate a basic mix-up in your knowledge base.

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