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Old 2010-02-16, 22:55   #188
flouran
 
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Quote:
Originally Posted by ET_ View Post
See post #185
Mea Culpa
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Old 2010-02-17, 00:16   #189
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Originally Posted by blob100 View Post
It is really easy to call me an "ignorant" but weren't you 14 years old?
Didn't you start too?
When I was 14 I listened to my teachers. I did not make
"conjectures", because I realized that I lacked knowledge to
do so intelligently.

When they suggested that something would be a good idea, I
followed their advice. When they told me to READ something, I did.

When they suggested that I did not know enough to pursue
something, I took their advice.

If you want to ask questions, go ahead. But you need to
reduce your arrogance. (e.g. claiming a conjecture as 'new' when
clearly you lacked knowledge to make such a judgment.)
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Old 2010-02-17, 01:17   #190
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Tomer,
When Bob uses the word ignorant, he means with out knowledge. If he wanted to say that you are not intelligent, he would. Knowing the meaning of ignorant is important.

Now that your initial idea has been dealt with, you do need to go and educate yourself. You also need to show restraint in dreaming up 'new' ideas until you have grown your knowledge base.
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Old 2010-02-17, 01:26   #191
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Quote:
Originally Posted by R.D. Silverman View Post
When I was 14 I listened to my teachers. I did not make
"conjectures", because I realized that I lacked knowledge to
do so intelligently.
You were a rare one, though. My favorite conjecture from my youth (by an 11-year-old CRGreathouse!), stated in modern/'adult' language:
The primes from 1 to n cannot be computed in time o(n^1.5).


Last fiddled with by CRGreathouse on 2010-02-17 at 01:27
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Old 2010-02-17, 09:43   #192
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Quote:
Originally Posted by blob100 View Post
I conjecture that: between n^2 to n^2+2n there is always a prime number.
So what did you do next? I hope you checked there were no small counter examples up to Ntested. I hope you googled to see if you could find anything similar (perhaps you need help in this category - that's a lesson for another day)

Next you should investigate how likely this is. For a big value of N, what's the probability this would be true "at random" or "by luck"? What's the probability it would be simultaneously true for all N above some point? This kind of analysis is called heuristics. It doesn't prove anything, but it gives you some insight about where to look. For example, if the probability gets very small for large N, then you need to check out some large values of N, whereas if it gets very small, that's probably a waste.

I don't know if you have the mathematical tools to work out these heuristics - they only require pre-college math, but at 14 years old you probably haven't yet learned everything in that category. Here are some hints to get you started:

1. Estimate the number of primes between N2 and N2+2n using the prime number theorem.
2. Use Step 1 to estimate the probability of zero primes in the range using the Poisson Approximation.
3. Use Step 2 to estimate the number of counter of examples for all N > Ntested, and approximate this sum with an integral.

I think you'll find it a learning experience to give these a try. Let us know how you come along. If you get stuck, post back with information about what you have tried and where you are stuck. See #29 in the ElevenSmooth Math FAQ if you need help with the Poisson Approximation

William
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Old 2010-02-17, 17:07   #193
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Quote:
Originally Posted by Uncwilly View Post
Tomer,
When Bob uses the word ignorant, he means with out knowledge. If he wanted to say that you are not intelligent, he would. Knowing the meaning of ignorant is important.

Now that your initial idea has been dealt with, you do need to go and educate yourself. You also need to show restraint in dreaming up 'new' ideas until you have grown your knowledge base.
I second this.

Bob's advice is sound, even though his delivery of said advice is almost always a disaster. Bob expects everyone to approach mathematics in the same way he did/does, is easily offended, and seems to be incapable of understanding how his behavior is received by people who are different than him.

Tomer, you seem to be fairly bright and overeager. I think you're confusing conjecturing with "making a conjecture". Conjecturing is great, and it means that you'll find interesting things to explore in mathematics, but as I'm sure you've noticed, many words outside of mathematics take on different meanings within mathematics, and "conjecture" is one of these terms. It takes quite a bit of mathematical maturity to make a good conjecture, because it requires breadth and depth of knowledge of the field. You're more likely to prove an unsolved problem before you will make a decent conjecture.
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Old 2010-02-17, 17:23   #194
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Quote:
Originally Posted by Uncwilly View Post
Tomer,
When Bob uses the word ignorant, he means with out knowledge. .

That is what the word ignorant means.

Why do you say "When Bob uses the word ignorant"??? Why
single me out? Do you use the word differently?? Do others?
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Old 2010-02-17, 17:31   #195
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Quote:
Originally Posted by CRGreathouse View Post
You were a rare one, though. My favorite conjecture from my youth (by an 11-year-old CRGreathouse!), stated in modern/'adult' language:
The primes from 1 to n cannot be computed in time o(n^1.5).

Ah. presumably you thought that the only way to do a prime test on n was
by trial division up to sqrt(n), and therefore testing all numbers up
to N would require at least O(N sqrt(N) time)?

Even now there are many areas of mathematics in which I would
not make a conjecture because of my ignorance.

The trouble with most 14 year olds is that are simply not aware of
how much they do not know. This can only be cured by reading, studying,
taking courses, and devoting lots and lots of time to understanding.
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Old 2010-02-17, 17:38   #196
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Quote:
Originally Posted by R.D. Silverman View Post
That is what the word ignorant means.

Why do you say "When Bob uses the word ignorant"??? Why
single me out? Do you use the word differently?? Do others?
Now you're showing your ignorance

Yes, others do use the word differently. It is frequently used perjoratively with shades of meaning including elements of "stupid", "impolite", "immature", "willfully perverse" and doubtless others.


Paul
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Old 2010-02-17, 17:52   #197
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Quote:
Originally Posted by xilman View Post
Now you're showing your ignorance

Yes, others do use the word differently. It is frequently used perjoratively with shades of meaning including elements of "stupid", "impolite", "immature", "willfully perverse" and doubtless others.


Paul
I am well aware that many people misuse many words. But the word
"ignorant" means "without knowledge". The fact that it is misused is a reflection of both ignorance and stupidity.

I would expect people in this forum not to make such a mistake.

Calling someone an ignoramus is a perjorative, because it means
"generally ignorant". But saying that someone is mathematically ignorant
is not and should not be a perjorative. It is a simple statement of fact.

I am more careful in my use of language. Especially in an academic
discussion.
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Old 2010-02-17, 18:07   #198
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Uncwilly was pointing out that when you use the word "ignorant",you use its proper meaning,whereas others tend to misuse it.

I don't know if i'm on Bob's "ignore list",or not,but I imagine I am.
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