20100216, 22:55  #188 
Dec 2008
7^{2}×17 Posts 

20100217, 00:16  #189  
Nov 2003
1D24_{16} Posts 
Quote:
"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.) 

20100217, 01:17  #190 
6809 > 6502
"""""""""""""""""""
Aug 2003
101Γ103 Posts
23×401 Posts 
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. 
20100217, 01:26  #191  
Aug 2006
174A_{16} Posts 
Quote:
The primes from 1 to n cannot be computed in time o(n^1.5). Last fiddled with by CRGreathouse on 20100217 at 01:27 

20100217, 09:43  #192  
"William"
May 2003
New Haven
2^{3}·5·59 Posts 
Quote:
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 precollege 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 N^{2} and N^{2}+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 > N_{tested}, 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 

20100217, 17:07  #193  
Cranksta Rap Ayatollah
Jul 2003
281_{16} Posts 
Quote:
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. 

20100217, 17:23  #194 
Nov 2003
1D24_{16} Posts 

20100217, 17:31  #195  
Nov 2003
1110100100100_{2} Posts 
Quote:
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. 

20100217, 17:38  #196  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
3×11^{2}×29 Posts 
Quote:
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 

20100217, 17:52  #197  
Nov 2003
16444_{8} Posts 
Quote:
"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. 

20100217, 18:07  #198 
Jan 2009
Ireland
2·3·31 Posts 
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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