## Search found 83 matches

- Fri Feb 03, 2017 12:17 pm UTC
- Forum: Mathematics
- Topic: Binary representation. Any number can be written as the sum of distinct powers of 2.
- Replies:
**4** - Views:
**2397**

### Binary representation. Any number can be written as the sum of distinct powers of 2.

Hi, I have the following sentence: Any number a can be written as the sum of distinct powers of 2. i.e. we can write: a = 2 k 1 + 2 k 2 + ... + 2 k n , where k 1 < k 2 < ... < k n . This is the binary representation of a. For example, the binary representation of 57 is 111001, since we can write 57 ...

- Mon Aug 10, 2015 7:06 pm UTC
- Forum: Mathematics
- Topic: Prove by induction 3^n < (n+2)!
- Replies:
**12** - Views:
**3270**

### Re: Prove by induction 3^n < (n+2)!

This may or may not be relevant to the case at hand (I just woke up and skimmed it), but some people consider N (the natural numbers) to be positive integers (1, 2, 3, ...) while others consider N to be the non-negative integers (0, 1, 2, ...). If things work as the book implies in the former case,...

- Mon Aug 10, 2015 6:28 pm UTC
- Forum: Mathematics
- Topic: Prove by induction 3^n < (n+2)!
- Replies:
**12** - Views:
**3270**

### Re: Prove by induction 3^n < (n+2)!

There is no 3! anywhere in your first post? 3 n+1 < (n+3)(n+2)! < (n+3)! we have written (n+3) in the place of 3. And also: n+3 > 3, therefore the direction of the inequality remains the same. And also, since n!=n(n-1)! we have (n+3)! = (n+3)(n+2)! it's ok that it is not true that n+3 > 3 (when n≥0...

- Mon Aug 10, 2015 5:55 pm UTC
- Forum: Mathematics
- Topic: Prove by induction 3^n < (n+2)!
- Replies:
**12** - Views:
**3270**

### Re: Prove by induction 3^n < (n+2)!

PeteP wrote:With n = 0 it's equal and with n>0 it's greater than 3. So it's >=.

Yes, obviously! But in the exercise I posted, there is n+3 > 3! Is a typo? I don't think so! Therefore, what are the elements that bring me to talk about n+3 ≥ 3? What is the reasoning that I have to do?

- Mon Aug 10, 2015 5:29 pm UTC
- Forum: Mathematics
- Topic: Prove by induction 3^n < (n+2)!
- Replies:
**12** - Views:
**3270**

### Re: Prove by induction 3^n < (n+2)!

thanks for the answer! If a < b, then 3a < (n+3)b even for n=0. ok, it's clear In other words, it is not true that n+3 > 3 (when n≥0). ok! It is only true that n+3 ≥ 3. But that's good enough because multiplying by the same thing on both sides also maintains inequalities. Sorry. Not clear! Forgive m...

- Mon Aug 10, 2015 4:53 pm UTC
- Forum: Mathematics
- Topic: Prove by induction 3^n < (n+2)!
- Replies:
**12** - Views:
**3270**

### Prove by induction 3^n < (n+2)!

Hi, I have the following exercise: Prove by induction the truth of the following statement: P(n) : 3 n < (n+2)! ( for all n in N ) The statement P(n) is true for n=0: 3 0 < (0+2)! 1 < 2 Assuming P(n) true for a particular value of n, from the truth of P(n) we will try to prove the truth of P(n+1). M...

- Sun Jun 14, 2015 10:44 am UTC
- Forum: Mathematics
- Topic: Permutations. Three digit numbers using 2,3,4,5,6,7,8,9.
- Replies:
**2** - Views:
**3066**

### Re: Permutations. Three digit numbers using 2,3,4,5,6,7,8,9.

Thanks!

The numbers in the exercise are the ones I have written in the first post. So, assuming that that numbers are right, are my answers right?

PeteP wrote:So I would re-check if it's maybe without the 6 or 8, since one might miss that.

The numbers in the exercise are the ones I have written in the first post. So, assuming that that numbers are right, are my answers right?

- Sat Jun 13, 2015 7:00 pm UTC
- Forum: Mathematics
- Topic: Permutations. Three digit numbers using 2,3,4,5,6,7,8,9.
- Replies:
**2** - Views:
**3066**

### Permutations. Three digit numbers using 2,3,4,5,6,7,8,9.

Hi, I have this exercise, I am not sure about the results because they are not the same of the ones given by the textbook. I don't know if there is a typo or an error in my calculations. Please, can you help me? How many numbers with three digits can be made using the digits {2,3,4,5,6,7,8,9} if: a)...

- Sat Jun 13, 2015 11:05 am UTC
- Forum: Mathematics
- Topic: Independent repeated trials and mutually exclusive events.
- Replies:
**4** - Views:
**1985**

### Re: Independent repeated trials and mutually exclusive event

In this exercise there are these outcomes, represented by WWW, WWT, etc. Think about what real life outcomes these letters represent. Is it possible for two of these outcomes, for example WWW and WWT, to occur simultaneously? Or is it always the case that if one of these outcomes has occurred, the ...

- Tue Jun 09, 2015 10:30 am UTC
- Forum: Mathematics
- Topic: Independent repeated trials and mutually exclusive events.
- Replies:
**4** - Views:
**1985**

### Re: Independent repeated trials and mutually exclusive event

Mutually exclusive is just a fancy term for saying that there is no overlap between the events. For instance, if I wanted to know the number of people in my class who are either women or math majors, I can't add the number of women to the number of math majors because that would double-count all th...

- Sun Jun 07, 2015 10:58 am UTC
- Forum: Mathematics
- Topic: Independent repeated trials and mutually exclusive events.
- Replies:
**4** - Views:
**1985**

### Independent repeated trials and mutually exclusive events.

Hi, I have the following exercise: A team wins (W) with probability 0.6, loses (L) with probability 0.3, and ties (T) with probability 0.1. Three games are played. Find the probability of A if the team wins at least twice and does not lose. In the set A there are all ordered triples with at least tw...

- Fri May 29, 2015 11:04 am UTC
- Forum: Computer Science
- Topic: Old programming language and databases
- Replies:
**4** - Views:
**4513**

### Re: Old programming language and databases

Many thanks for the answer. Lacking that, if the language has the ability to open TCP/IP connections, you could talk to the DB server directly. The network protocols are usually well documented and could in theory be reimplemented. "Reimplementing" sounds like a lot of effort - we're talki...

- Thu May 28, 2015 11:04 am UTC
- Forum: Computer Science
- Topic: Old programming language and databases
- Replies:
**4** - Views:
**4513**

### Old programming language and databases

Hi, Please, I would to know, having an old programming language, for example Pascal, Qbasic, or GwBasic etc..., and a database like MySql or something else, Is it possible to create a program in those languages for querying to that database? Certainly I don't want the list of the source code of some...

- Tue May 19, 2015 5:51 pm UTC
- Forum: Mathematics
- Topic: Statistics. Conditional probability and percentage.
- Replies:
**4** - Views:
**1985**

### Statistics. Conditional probability and percentage.

Hi, I have the following exercise on conditional probability: Suppose 60% of the freshmen class of a college are women. Furthermore, suppose 25% of the men and 10% of the women in the class are studying mathematics. A freshman student is chosen at random. Find the probability that: The student is st...

- Tue May 19, 2015 5:27 pm UTC
- Forum: Mathematics
- Topic: Conditional probability and multiplication theorem
- Replies:
**5** - Views:
**2193**

### Re: Conditional probability and multiplication theorem

Wildcard wrote:Wow, Venn diagrams to represent a marbles probability question. That seems...needlessly complicated....

Yeah I know! But I wanted to know exactly what happen drawing a Venn diagram having a conditional probability!

Wildcard wrote:Does that help?

yes, really, many thanks for the answer! it helps a lot!

- Tue Apr 28, 2015 11:08 am UTC
- Forum: Mathematics
- Topic: Conditional probability and multiplication theorem
- Replies:
**5** - Views:
**2193**

### Re: Conditional probability and multiplication theorem

I have tried to draw a Venn diagram, let me know what do you think! I have considered some ordered triples as (a,b,c) where: a = marble in the first draw; b = marble in the second draw; c = marble in the third draw; I have considered the following sets: A = all the triples with the RED marble on FIR...

- Sun Apr 19, 2015 6:36 pm UTC
- Forum: Mathematics
- Topic: Conditional probability and multiplication theorem
- Replies:
**5** - Views:
**2193**

### Re: Conditional probability and multiplication theorem

I want to put another question. We have a sample space S, and let A an event that depends from event B. We will have that the probability of A is: P(A|B) = P(A∩B)/P(B) My question is simple: is it correct to consider the results of the event B as a "new sample space" for the event A? or th...

- Fri Apr 17, 2015 5:36 pm UTC
- Forum: Mathematics
- Topic: Conditional probability and multiplication theorem
- Replies:
**5** - Views:
**2193**

### Conditional probability and multiplication theorem

Hi, I have this exercise: A box contains 7 red marbles and 3 white marbles. Three marbles are drawn from the box one after the other. Find the probability p that the first two are red, and the third is white. p = (7/10)(6/9)(3/8) = 7/40 it's clear the exercise, but I got some problems on understandi...

- Mon Mar 23, 2015 7:56 pm UTC
- Forum: Mathematics
- Topic: Probability of selecting the winner betting on 2 out of 5
- Replies:
**8** - Views:
**2326**

### Probability of selecting the winner betting on 2 out of 5

Hi, I have this exercise about probability. But I have not understand the reasoning followed. This is the problem: 5 horses are in a race. John bets on 2 of them. Find the probability p that John picked the winner. This is the solved example: There are C(5,2)=10 ways to select 2 of the horses. Four ...

- Thu Mar 19, 2015 12:00 pm UTC
- Forum: Mathematics
- Topic: Probability.Addition rule,inclusive or,at least one of three
- Replies:
**4** - Views:
**1883**

### Probability.Addition rule,inclusive or,at least one of three

Hi, I have the following problem: A student has three probability to pass three exams. Respectively, 3/4, 2/3 and 1/2. What is the probability that she will pass at least one of these three exams? So it is analog to say: "What is the probability that she will pass either the first OR the second...

- Sun Mar 08, 2015 12:51 pm UTC
- Forum: Mathematics
- Topic: Combinatorics. Select spaces to put letters.
- Replies:
**2** - Views:
**1267**

### Combinatorics. Select spaces to put letters.

Hi, considering the word GAINER, what is the possible number of arrangements without letting the two letters A,R be together? I go to consider the letters different from A,R, inserting one space between them where I can insert the two letters I said before. _ G _ I _ N _ E _ 1) in the following reas...

- Fri Mar 06, 2015 6:49 pm UTC
- Forum: Mathematics
- Topic: Combinatorics. Selecting identical or different things.
- Replies:
**2** - Views:
**1243**

### Combinatorics. Selecting identical or different things.

Hi, I have a simple question: 1) having 6 spaces and 5 identical things: I can put the 5 things in the 6 spaces in C(6,5)=6 different ways. 2) having 6 spaces, 4 identical things and 1 another thing different from the other four: I can put them in the 6 spaces in (6)*C(5,4)=30 different ways. can yo...

- Fri Feb 27, 2015 12:05 pm UTC
- Forum: Mathematics
- Topic: Combinatorics.Exclude when specific thing is before another.
- Replies:
**2** - Views:
**1368**

### Combinatorics.Exclude when specific thing is before another.

Hi, I have some problems with this exercise about combinatorics. Please can you help me to resolve that? : Five guys: John, Jack, Greg, Matt, Eric, will be speaking at a meeting. How many ways can they take their turn without Jack speaking before John? [Answer: 60] I have done my own reasoning, as f...

- Mon Jun 17, 2013 12:48 am UTC
- Forum: Mathematics
- Topic: Validity of deductive arguments involving "if" and "then"
- Replies:
**11** - Views:
**1739**

### Re: Validity of deductive arguments involving "if" and "then

He didn't say "it's raining but John has no umbrella" is false, he said "If it's raining, John has an umbrella" is false when "it's raining but John has no umbrella" is true. yes I wrote the wrong thing! So: Do you establishing what you said on a linguistic/grammatical...

- Sun Jun 16, 2013 10:02 am UTC
- Forum: Mathematics
- Topic: Validity of deductive arguments involving "if" and "then"
- Replies:
**11** - Views:
**1739**

### Re: Validity of deductive arguments involving "if" and "then

thanks! :wink: When P is true, it's obvious: "If it's raining, John has an umbrella" is true when it's raining and John has an umbrella, and it's false when it's raining but John has no umbrella. Simple questions derive from the above. Do you establishing what you said on a linguistic/gram...

- Mon Jun 10, 2013 10:46 am UTC
- Forum: Mathematics
- Topic: Validity of deductive arguments involving "if" and "then"
- Replies:
**11** - Views:
**1739**

### Validity of deductive arguments involving "if" and "then"

I have some doubts, so can you help me please? Doing some edits to the truth table P->Q for the conditional statement, we would end up with incorrect conclusions. Having the following argument: P->Q P Therefore Q This type of argument is correct and the following table confirm this: Premises Conclus...

- Mon May 27, 2013 12:42 am UTC
- Forum: Language/Linguistics
- Topic: "both have" or "have both" ?
- Replies:
**9** - Views:
**4641**

### Re: "both have" or "have both" ?

Ok, you have resolved the problem of double negatives, even if I have not asked about it! and it's ok! :) thanks! I'm sorry, but I don't quite understand what you're asking here in my 1) statement 1) I will not have both fish and potatoes. we have said that it is right to consider this: I will have ...

- Sun May 26, 2013 8:49 pm UTC
- Forum: Language/Linguistics
- Topic: "both have" or "have both" ?
- Replies:
**9** - Views:
**4641**

### Re: "both have" or "have both" ?

thank you very much indeed! :D The second sentence is not grammatically correct, however, because word order is so important in English. If you place the word "both" in that position in the sentence, it tends to reflect back on the subject - and, since the subject is only one person ("...

- Sun May 26, 2013 11:08 am UTC
- Forum: Language/Linguistics
- Topic: "both have" or "have both" ?
- Replies:
**9** - Views:
**4641**

### "both have" or "have both" ?

Hi, I have these sentences: 1) I will not have both fish and potatoes. 2) I will not both have fish and potatoes. I know that 1) is correct, i would to know if also the 2) is correct. And also what's the meaning of the two sentences? for example in the 1) the correct meaning would be: I will have on...

- Tue Jan 15, 2013 7:33 pm UTC
- Forum: Mathematics
- Topic: Subgroups of an arbitrary group
- Replies:
**9** - Views:
**3610**

### Re: Subgroups of an arbitrary group

Ok! thank you very much mike-l !

- Wed Jan 09, 2013 11:29 am UTC
- Forum: Mathematics
- Topic: Subgroups of an arbitrary group
- Replies:
**9** - Views:
**3610**

### Re: Subgroups of an arbitrary group

Talith wrote:Let G be a group. Let H and K be subgroups of G. 1) What is the definition of H and K being subgroups of G? 1) >H,K must be non-empty subsets of G. >The result of a particular operation * on every couple of elements in H, and every couple of elements in K, must exists in H,K. If this l...

- Thu Dec 13, 2012 5:38 pm UTC
- Forum: Mathematics
- Topic: Subgroups of an arbitrary group
- Replies:
**9** - Views:
**3610**

### Re: Subgroups of an arbitrary group

Thank you very much Talith for your suggestions, I will take your advice to heart! :D I have tried this: If you find this ok, you might like to try this follow up question. Let G be a group and let g be an element of G. We define a subset called the 'centraliser' of g in G which is comprised of all ...

- Sun Dec 09, 2012 12:29 pm UTC
- Forum: Mathematics
- Topic: Subgroups of an arbitrary group
- Replies:
**9** - Views:
**3610**

### Re: Subgroups of an arbitrary group

I post here another exercise with my own resolution, and please, I would want to know if it is correct! I don't know if is opportune to create another thread, correct me if I'm wrong, but I don't think so, since the argument is again about Subgroups of an arbitrary group. Exercise: By the center of ...

- Wed Nov 28, 2012 7:05 pm UTC
- Forum: Mathematics
- Topic: Subgroups of an arbitrary group
- Replies:
**9** - Views:
**3610**

### Re: Subgroups of an arbitrary group

thank you very much for your helping hand Talith. I am grateful to you. :D Let G be a group. Let H and K be subgroups of G. 1) What is the definition of H and K being subgroups of G? 1) >H,K must be non-empty subsets of G. >The result of a particular operation * on every couple of elements in H, and...

- Wed Nov 21, 2012 11:59 am UTC
- Forum: Mathematics
- Topic: Subgroups of an arbitrary group
- Replies:
**9** - Views:
**3610**

### Subgroups of an arbitrary group

Hi, I have this Excercise about Subgroups of an arbitrary group, and I hope in some helping hand to try to resolve it rightly. Let G be a group. Prove the following: If H and K are subgroups of a group G, prove that H∩K is a subgroup of G. (Remember that x in H∩K iff x in H AND x in K) So now post h...

- Mon Nov 19, 2012 11:07 am UTC
- Forum: Mathematics
- Topic: Subgroups of functions and of abelian groups. Excercises.
- Replies:
**8** - Views:
**2951**

### Re: Subgroups of functions and of abelian groups. Excercises

thanks! >is it right the previous prove by induction? But I have doubt to prove that even if I commute the exponents, the result is the same... Now I return to talk about some previous posts: Another important but subtle point: In order to show that a subset of a group is a subgroup. You have to sho...

- Sat Nov 17, 2012 11:07 am UTC
- Forum: Mathematics
- Topic: Subgroups of functions and of abelian groups. Excercises.
- Replies:
**8** - Views:
**2951**

### Re: Subgroups of functions and of abelian groups. Excercises

To show this, you can probably use the following proposition which you've either been shown in class or been asked to prove on a problem sheet. (If not, go ahead and prove it) Let G be a group. Let x be in G. For all k,l in the integers, (x k ) l =x kl =x lk =(x l ) k So I tried to prove that: (a n...

- Fri Nov 16, 2012 12:08 pm UTC
- Forum: Mathematics
- Topic: Powers and Roots of Group Elements. Excercise.
- Replies:
**14** - Views:
**3277**

### Re: Powers and Roots of Group Elements. Excercise.

Looking at what I have done: a 2 = e (aa)(aa -1 ) = e aaaa -1 a = a aaa = a so the steps 2 and 3 are completely useless. Fastly, it should had been also right, if from the first step I had multiplied by "a" both members with no problems... so the right resolution of the exercise become thi...

- Fri Nov 16, 2012 11:50 am UTC
- Forum: Mathematics
- Topic: Simple question about induction.
- Replies:
**6** - Views:
**1538**

### Simple question about induction.

Why when I go to demonstrate this identity by induction 1 + 2 + 3 + ... + (n-1) + n = n(n+1)/2 for each n >=1 I have seen that I can do that for (n-1) or (n+1)! So, what I want to know in this thread is very simple: In general: >how can I detect the right way to proceed? >In what situation I would u...

- Fri Nov 16, 2012 12:36 am UTC
- Forum: Mathematics
- Topic: Powers and Roots of Group Elements. Excercise.
- Replies:
**14** - Views:
**3277**

### Re: Powers and Roots of Group Elements. Excercise.

Xenomortis wrote:What, precisely, is it the question wants you to prove?

Is it just:

If a^{2}= 1 then there exists g s.t. g^{3}= a?

Yes!

So you have only multiplied both member by a

aa = e

aaa = a

Therefore, does my proceeding have been long with those steps?