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 Post subject: What makes a good teacher? What is a formula?
Post #1 Posted: Sun Feb 16, 2020 9:50 am 
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@Marcel
And what if student refuse to do what teacher say? In my life, i meet many bad teachers, and even if some skilled ppl were nominally taught by them, after the teacher-student relation were over (sometimes even before), they always said "He didnt taught me anything, i learned all by myself". And i am not talking only about go, i say it generally.

I still remember one of math teachers in my elemenatry school which was saying that "there is no formula for producing n-th prime number [f(n)=n-th prime number]". When i started to study math i accidentaly ran into article that extensively deal with prime numbers and many formulas and theorem about them. It also contained many formulas that this math teacher denied existence. I wouldnt reccomend that math teacher to even my enemies.

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 Post subject: Re: Shin Jinseo's Study Plan
Post #2 Posted: Sun Feb 16, 2020 10:08 am 
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A good teacher is someone who motivates students to learn, but students have to do the ...k.

The fact that "there is no formula for producing n-th prime number [f(n)=n-th prime number]" is correct, but the teacher could have said that f(n) ~ n log(n), maybe this would have fascinated part of his audience.


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 Post subject: Re: Shin Jinseo's Study Plan
Post #3 Posted: Sun Feb 16, 2020 10:53 am 
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Quote:
A good teacher is someone who motivates students to learn, but students have to do the ...k.


An excellent soccer example today on the BBC site:

https://www.bbc.co.uk/news/av/uk-515164 ... od-teacher

A written version is at:

https://www.bbc.co.uk/programmes/articl ... land-discs

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 Post subject: Re: Shin Jinseo's Study Plan
Post #4 Posted: Sun Feb 16, 2020 11:05 am 
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AloneAgainstAll wrote:
I still remember one of math teachers in my elemenatry school which was saying that "there is no formula for producing n-th prime number [f(n)=n-th prime number]". When i started to study math i accidentaly ran into article that extensively deal with prime numbers and many formulas and theorem about them. It also contained many formulas that this math teacher denied existence. I wouldnt reccomend that math teacher to even my enemies.


Too bad. I don't know about his teaching ability, but he was right about the non-existence of a prime number formula that does not include listing some of them. Oh, sure, you can come up with a formula, f(n), where n is a natural number, that produces all the prime numbers up to 41, but the next value is not a prime. In fact, there is a polynomial that will produce the sequence of all known primes. So what?

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 Post subject: Re: Shin Jinseo's Study Plan
Post #5 Posted: Sun Feb 16, 2020 11:07 am 
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jlt wrote:
The fact that "there is no formula for producing n-th prime number [f(n)=n-th prime number]" is correct, but the teacher could have said that f(n) ~ n log(n), maybe this would have fascinated part of his audience.


Well, since they were in elementary school, some of them might have fallen off the log. ;)

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 Post subject: Re: Shin Jinseo's Study Plan
Post #6 Posted: Sun Feb 16, 2020 11:18 am 
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Ah, I missed the word "elementary". But anyway, my point was that the role of the teacher is to sow seeds. Not every seed will grow into a plant, but some will.


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 Post subject: Re: Shin Jinseo's Study Plan
Post #7 Posted: Sun Feb 16, 2020 5:40 pm 
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jlt wrote:
A good teacher is someone who motivates students to learn, but students have to do the ...k.

The fact that "there is no formula for producing n-th prime number [f(n)=n-th prime number]" is correct, but the teacher could have said that f(n) ~ n log(n), maybe this would have fascinated part of his audience.



Jlt why are you sure that there is no such a formula? Can you elaborate what makes you think that way, or who told you that, or where you heard that, or what is proof that such a formula does not exist? I am most anxious to hear all of this, and i am not telling it with sarcasm or disrespect, or any hostility (everybody who thinks same would be greatly apprecisted if provide me answers for this questions).

Here in attachment is one of such a formulas you just denied existence, you can check that it indeed works (but pls check it after you respond to my questions, its really important to me.


Attachments:
File comment: Formula i mentioned
Nth prime number formula 44.png
Nth prime number formula 44.png [ 4.51 KiB | Viewed 757 times ]
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 Post subject: Re: Shin Jinseo's Study Plan
Post #8 Posted: Sun Feb 16, 2020 6:12 pm 
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Bill Spight wrote:

Too bad. I don't know about his teaching ability, but he was right about the non-existence of a prime number formula that does not include listing some of them. Oh, sure, you can come up with a formula, f(n), where n is a natural number, that produces all the prime numbers up to 41, but the next value is not a prime. In fact, there is a polynomial that will produce the sequence of all known primes. So what?


Unfortunately your claim that this teacher was right is completely wrong. Do you have any argument to back up your words?

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 Post subject: Re: Shin Jinseo's Study Plan
Post #9 Posted: Sun Feb 16, 2020 6:41 pm 
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AloneAgainstAll wrote:
Unfortunately your claim that this teacher was right is completely wrong. Do you have any argument to back up your words?


Your formula is completly useless. It's order of magnitude worse than a naive algorithm and don't give any theorical insight on the problem (as the [-{k/i}] is just a fancy way to test if i divide k).

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 Post subject: Re: Shin Jinseo's Study Plan
Post #10 Posted: Sun Feb 16, 2020 6:51 pm 
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Tryss wrote:
AloneAgainstAll wrote:
Unfortunately your claim that this teacher was right is completely wrong. Do you have any argument to back up your words?


Your formula is completly useless. It's order of magnitude worse than a naive algorithm and don't give any theorical insight on the problem (as the [-{k/i}] is just a fancy way to test if i divide k).


But its correct, right?Did i ever said its usefull for computing prime numbers? We talk about existence and correctness, not usefulness, right?

If i didnt convinced you, think about this way - lets say i have completely unusefull formula which produce nontrivial zeros of Riemman-Zeta function. Would you be interested to see it, or would you just say, its useless for computing them?

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 Post subject: Re: Shin Jinseo's Study Plan
Post #11 Posted: Sun Feb 16, 2020 8:46 pm 
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AloneAgainstAll wrote:
Here in attachment is one of such a formulas you just denied existence, you can check that it indeed works (but pls check it after you respond to my questions, its really important to me.


What do you mean when you say that the formula works?

Thanks. :)

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 Post subject: Re: Shin Jinseo's Study Plan
Post #12 Posted: Sun Feb 16, 2020 9:02 pm 
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It means that for any natural number n, this formula produce n-th prime number.

I thought that meaning of "formula works" is same as "this formula is correct (produce correct results, produce results expected)", but i guess thats not the same.

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 Post subject: Re: Shin Jinseo's Study Plan
Post #13 Posted: Sun Feb 16, 2020 10:34 pm 
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AloneAgainstAll wrote:
It means that for any natural number n, this formula produce n-th prime number.

I thought that meaning of "formula works" is same as "this formula is correct (produce correct results, produce results expected)", but i guess thats not the same.


Well, since you mentioned plural formulae, there could be a different way for each formula to work. :)

What is the simplest formula that works?

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The Adkins Principle:
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Banana Republic. It's not just a store anymore.

Everything with love. Stay safe.


Last edited by Bill Spight on Sun Feb 16, 2020 10:45 pm, edited 1 time in total.
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 Post subject: Re: Shin Jinseo's Study Plan
Post #14 Posted: Sun Feb 16, 2020 10:43 pm 
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Heureka, I found the meaning of life.
It is the "meaning of life"!

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 Post subject: Re: Shin Jinseo's Study Plan
Post #15 Posted: Sun Feb 16, 2020 10:47 pm 
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Gomoto wrote:
Heureka, I found the meaning of life.
It is the "meaning of life"!


Elvis lives. :D

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 Post subject: Re: Shin Jinseo's Study Plan
Post #16 Posted: Sun Feb 16, 2020 11:33 pm 
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primes = #@!?b + primes - #@!?b

the interesting idendities are the ones with different left and right sides. :-)

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 Post subject: Re: Shin Jinseo's Study Plan
Post #17 Posted: Sun Feb 16, 2020 11:37 pm 
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Bill Spight wrote:

What is the simplest formula that works?


This is argument which is backing up your claim? I must admit, i expected sth much better.

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 Post subject: Re: Shin Jinseo's Study Plan
Post #18 Posted: Mon Feb 17, 2020 12:35 am 
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AloneAgainstAll: your formula is correct, but doesn't do the job that one would expect from a formula. This conversation is a bit like:

- Go Master: assuming komi is (fair komi + 0.5), there is no known method to win a go game as white 100% of the time.

- StudentAloneAgainstAll: I disagree. You can explore the entire tree and search for an optimal path.


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 Post subject: Re: Shin Jinseo's Study Plan
Post #19 Posted: Mon Feb 17, 2020 1:13 am 
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You really think this is good paraphrase? I dont think so. There are things we cant "enclose" in mathemathical formulas (like results of integral of sin(x^2) cant be described by elementary functions, only infinite sum ) etc. So the fact that we can produce such a formula (even if its completely useless for computing) is mathemathically significant.

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 Post subject: Re: Shin Jinseo's Study Plan
Post #20 Posted: Mon Feb 17, 2020 1:35 am 
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What is significant and what is not is a matter of personal taste. So let's agree that we disagree here...

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