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Gallien Contemporary Abstract Algebra, section 20, problem 2 (not homework, I'm working through all the exercises in the book, but I've been off a while, so I'm probably making some really stupid error). Show that . I'm thinking that I should be writing elements of the first form as and the second as but it seems that this is very unlikely as a means of getting to the solution. Then trying to use , but shouldn't that require that be a zero of ? Any hints on getting to the solution (for the love of God, please don't just give me an answer, I want to find it myself). 68.183.18.54 ( talk) 00:37, 5 January 2008 (UTC)
Suppose you have 4 random variables (a,b,c,d) used to generate a line segment with two endpoints ((a,b) & (c,d)). All four variables must be within 0 and 1. What is the average length of said line segment? I think it would have to be μ√((a-c)2+(b-d)2) but have no clue as to how to evaluate that.
By the way this isn't homework, it's just a problem I've been thinking about for a while. Thanks in advance for any help. 65.31.80.94 ( talk) 02:35, 5 January 2008 (UTC)
I've heard that in mathematics and according to mathematicians, any chance or probability below one out of 1050 is counted and dismissed as "impossible" or "never happening". Why? Are there any articles or section of articles in Wikipedia about this? Bowei Huang ( talk) 03:06, 5 January 2008 (UTC)
I would think that the OP got that from some other discipline, I can't imagine any mathematician making that statement. In Project Management, the 6Σ method is considered to be pretty neat, ie near certainty (and yes, I know it should be a lower case sigma, but QA people always write it that way). But 6σ is only .9999999980268 which equates to a probability of 1 in 5x108 approximately. And even 7σ is still only .9999999999974 (1 in 3.8x1011). In my own discipline, when I was still a design engineer we used slide rules (showing my age) which are good to three significant figures, ie any variation greater than 1 in 103 was not considered significant. Can't think who would be interested out to 1 in 1050 though. SpinningSpark 15:12, 5 January 2008 (UTC)
I have done a little poking around over this 1050 number and think I have the answer. It comes up a lot on Creationist web sites as the largest number that can occur in nature, the implication being that anything that has a larger number of possibilities is not going to happen. See for instance this one [1] under the MATHEMATICAL POSSIBILITIES OF DNA section. SpinningSpark 17:52, 5 January 2008 (UTC)
I've heard that there's something called Borel's Law of Mathematics. What is that? Bowei Huang ( talk) 05:51, 8 January 2008 (UTC)
Where have you heard or thought of that? And what about the probability of a tornado assembling a Boeing 747 out of pieces from a junkyard? Bowei Huang ( talk) 01:23, 9 January 2008 (UTC)
But suppose the junkyard did have all the materials and chemicals to build an airplane piled together? Bowei Huang ( talk) 02:19, 9 January 2008 (UTC)
Thanks for the last answer.
I'm doing another question now which never works out its on Conditional Probability. one example is There a 4 firms biding for a contract, A, B, C, & D. The probabilities of each wining is as follows :- P(A)=0.15, P(B)=0.35, P(C)=0.3, P(D)=0.2. However firm A drops out. Find the new probability of B wining.
I did it like this
P(B|Ā)= P(B :upsidedown U: Ā) ---------------------- P(B)
= 0.35 + 0.85 ----------- 0.85 = 1.412
Thats clearly wrong, so what do I do? 136.206.1.17 ( talk) 15:29, 5 January 2008 (UTC)
Should it be, P(B & Ā) = P(B) X P(Ā) on the top line? If thats the case the answer works out a .35, also wrong as it should be going up.
If I did the sum like this I get a realistic answer, is it right?
P(A)= 0.35 --------------- 0.35 + 0.3 + 0.2 =0.538
unsigned contribution by 136.206.1.17 ( talk)
You said thanks for the last answer, but I looked at your previous post and noticed that no-one has actually given you the correct answer yet, only hints (meanies!). Have you got it now or do you want me to put you out of your misery? SpinningSpark 16:32, 5 January 2008 (UTC)
Can you put me out of my misory please? 136.206.1.17 ( talk) 16:35, 5 January 2008 (UTC)
Thanks for that answer. I know its a conditional probability question because thats the section of my book that it comes from. —Preceding unsigned comment added by 78.16.6.199 ( talk) 12:20, 6 January 2008 (UTC)
Hello. I need some help with formal logic principles, as they relate to language. In formal logic, there is a strong connection between math and language. In particular, using the language "and" versus the language "or" logically carries two very different meanings.
So, let's say that we consider classifying everyone in the world into the following two characteristics: Athlete (professional) and Black.
Using these two characteristics, we effectively have four distinct categories of people:
Using formal logic, these would be described as
Using set theory notation, these would be described as
Now ... to distinguish between the language of AND versus the language of OR:
A AND B
If we discuss Set A intersect Set B ... in logic, A AND B ... we are talking about people who are Athletes AND are also Black ... that is, a person must display BOTH characteristics
So, let us consider the four famous people named above
A OR B
If we discuss Set A union Set B ... in logic, A OR B ... we are talking about people who are either Athletes OR are Black OR both ... that is, a person must display either ONE characteristic OR the other OR perhaps both
So, let us consider the four famous people named above
Conclusion:
Using "and" ... A AND B ... this includes only 1 person from our group (Tyson) and excludes the other 3 people (Giambi, Washington, Cruise)
Using "or" ... A OR B ... this excludes only 1 person from our group (Cruise) and includes the other 3 people (Giambi, Washington, Tyson)
Thus, the word "and" versus "or" has very different meanings.
So, before I continue ... is all of the above correct? Or am I missing anything?
Premises: We can assume for this discussion that the Universe of consideration (U) is just these four famous individuals for now ... and that the word "or" is the inclusive or (OR) as opposed to the exclusive or (XOR) ... and that both Sets (Athletes / Black) are well-defined sets.
Thank you! ( Joseph A. Spadaro ( talk) 19:19, 5 January 2008 (UTC))
Thanks. So, it seems that we are all more or less on the same page. That being said ... I posted a question on the Language Help Desk. And I wanted to get some input/feedback from some mathematicians who understand logic ... and the interplay between formal logic and precise language. If anyone well versed in math / formal logic would take a look at this question on the Language Desk ( Wikipedia:Reference desk/Language#Correct wording), and offer some input there, it would be appreciated. Thanks. ( Joseph A. Spadaro ( talk) 23:23, 6 January 2008 (UTC))
Thanks for the input --- much appreciated ... ( Joseph A. Spadaro ( talk) 06:03, 10 January 2008 (UTC))
Mathematics desk | ||
---|---|---|
< January 4 | << Dec | January | Feb >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Gallien Contemporary Abstract Algebra, section 20, problem 2 (not homework, I'm working through all the exercises in the book, but I've been off a while, so I'm probably making some really stupid error). Show that . I'm thinking that I should be writing elements of the first form as and the second as but it seems that this is very unlikely as a means of getting to the solution. Then trying to use , but shouldn't that require that be a zero of ? Any hints on getting to the solution (for the love of God, please don't just give me an answer, I want to find it myself). 68.183.18.54 ( talk) 00:37, 5 January 2008 (UTC)
Suppose you have 4 random variables (a,b,c,d) used to generate a line segment with two endpoints ((a,b) & (c,d)). All four variables must be within 0 and 1. What is the average length of said line segment? I think it would have to be μ√((a-c)2+(b-d)2) but have no clue as to how to evaluate that.
By the way this isn't homework, it's just a problem I've been thinking about for a while. Thanks in advance for any help. 65.31.80.94 ( talk) 02:35, 5 January 2008 (UTC)
I've heard that in mathematics and according to mathematicians, any chance or probability below one out of 1050 is counted and dismissed as "impossible" or "never happening". Why? Are there any articles or section of articles in Wikipedia about this? Bowei Huang ( talk) 03:06, 5 January 2008 (UTC)
I would think that the OP got that from some other discipline, I can't imagine any mathematician making that statement. In Project Management, the 6Σ method is considered to be pretty neat, ie near certainty (and yes, I know it should be a lower case sigma, but QA people always write it that way). But 6σ is only .9999999980268 which equates to a probability of 1 in 5x108 approximately. And even 7σ is still only .9999999999974 (1 in 3.8x1011). In my own discipline, when I was still a design engineer we used slide rules (showing my age) which are good to three significant figures, ie any variation greater than 1 in 103 was not considered significant. Can't think who would be interested out to 1 in 1050 though. SpinningSpark 15:12, 5 January 2008 (UTC)
I have done a little poking around over this 1050 number and think I have the answer. It comes up a lot on Creationist web sites as the largest number that can occur in nature, the implication being that anything that has a larger number of possibilities is not going to happen. See for instance this one [1] under the MATHEMATICAL POSSIBILITIES OF DNA section. SpinningSpark 17:52, 5 January 2008 (UTC)
I've heard that there's something called Borel's Law of Mathematics. What is that? Bowei Huang ( talk) 05:51, 8 January 2008 (UTC)
Where have you heard or thought of that? And what about the probability of a tornado assembling a Boeing 747 out of pieces from a junkyard? Bowei Huang ( talk) 01:23, 9 January 2008 (UTC)
But suppose the junkyard did have all the materials and chemicals to build an airplane piled together? Bowei Huang ( talk) 02:19, 9 January 2008 (UTC)
Thanks for the last answer.
I'm doing another question now which never works out its on Conditional Probability. one example is There a 4 firms biding for a contract, A, B, C, & D. The probabilities of each wining is as follows :- P(A)=0.15, P(B)=0.35, P(C)=0.3, P(D)=0.2. However firm A drops out. Find the new probability of B wining.
I did it like this
P(B|Ā)= P(B :upsidedown U: Ā) ---------------------- P(B)
= 0.35 + 0.85 ----------- 0.85 = 1.412
Thats clearly wrong, so what do I do? 136.206.1.17 ( talk) 15:29, 5 January 2008 (UTC)
Should it be, P(B & Ā) = P(B) X P(Ā) on the top line? If thats the case the answer works out a .35, also wrong as it should be going up.
If I did the sum like this I get a realistic answer, is it right?
P(A)= 0.35 --------------- 0.35 + 0.3 + 0.2 =0.538
unsigned contribution by 136.206.1.17 ( talk)
You said thanks for the last answer, but I looked at your previous post and noticed that no-one has actually given you the correct answer yet, only hints (meanies!). Have you got it now or do you want me to put you out of your misery? SpinningSpark 16:32, 5 January 2008 (UTC)
Can you put me out of my misory please? 136.206.1.17 ( talk) 16:35, 5 January 2008 (UTC)
Thanks for that answer. I know its a conditional probability question because thats the section of my book that it comes from. —Preceding unsigned comment added by 78.16.6.199 ( talk) 12:20, 6 January 2008 (UTC)
Hello. I need some help with formal logic principles, as they relate to language. In formal logic, there is a strong connection between math and language. In particular, using the language "and" versus the language "or" logically carries two very different meanings.
So, let's say that we consider classifying everyone in the world into the following two characteristics: Athlete (professional) and Black.
Using these two characteristics, we effectively have four distinct categories of people:
Using formal logic, these would be described as
Using set theory notation, these would be described as
Now ... to distinguish between the language of AND versus the language of OR:
A AND B
If we discuss Set A intersect Set B ... in logic, A AND B ... we are talking about people who are Athletes AND are also Black ... that is, a person must display BOTH characteristics
So, let us consider the four famous people named above
A OR B
If we discuss Set A union Set B ... in logic, A OR B ... we are talking about people who are either Athletes OR are Black OR both ... that is, a person must display either ONE characteristic OR the other OR perhaps both
So, let us consider the four famous people named above
Conclusion:
Using "and" ... A AND B ... this includes only 1 person from our group (Tyson) and excludes the other 3 people (Giambi, Washington, Cruise)
Using "or" ... A OR B ... this excludes only 1 person from our group (Cruise) and includes the other 3 people (Giambi, Washington, Tyson)
Thus, the word "and" versus "or" has very different meanings.
So, before I continue ... is all of the above correct? Or am I missing anything?
Premises: We can assume for this discussion that the Universe of consideration (U) is just these four famous individuals for now ... and that the word "or" is the inclusive or (OR) as opposed to the exclusive or (XOR) ... and that both Sets (Athletes / Black) are well-defined sets.
Thank you! ( Joseph A. Spadaro ( talk) 19:19, 5 January 2008 (UTC))
Thanks. So, it seems that we are all more or less on the same page. That being said ... I posted a question on the Language Help Desk. And I wanted to get some input/feedback from some mathematicians who understand logic ... and the interplay between formal logic and precise language. If anyone well versed in math / formal logic would take a look at this question on the Language Desk ( Wikipedia:Reference desk/Language#Correct wording), and offer some input there, it would be appreciated. Thanks. ( Joseph A. Spadaro ( talk) 23:23, 6 January 2008 (UTC))
Thanks for the input --- much appreciated ... ( Joseph A. Spadaro ( talk) 06:03, 10 January 2008 (UTC))