|
Species5618
Yellow-bellied Woodpecker
Joined: Apr 18, 2012
Posts: 55
|
 Posted: Sun Apr 29, 2012 9:43 am Post subject: |
 |
|
| Declension wrote: | | cubedemon6073 wrote: | | If we have a/b=c. a has to be a real number. b has to be a real number that is a nonzero number. c is a real number. These are our constraints for division. |
That's right. Actually (you can safely ignore this if you want) there is an extension of the real numbers called the complex numbers, and we can extend the definition of division so that a can be any complex number, b can be any nonzero complex number, and c ends up being a complex number. But note that even in this extension, we still do not define "a / b" when b is zero. |
The operation of division "a / b = c" is defined in any so-called "division ring". A ring is a mathematical structure with 2 operations working on it (called addition and multiplication) satisfying a list of properties. The most common example of a ring is the reals. The reals have addition and multiplication defined in the usual way. The list of properties that these operations have to satisfy (See Wikipedia for details) are of course satisfied. Each ring has 2 special elements: The additive unity (the element that when added to another element doesn't change it. For the reals, this is zero) and the multiplicative unity (the element that when multiplied with another element doesn't change it. For the reals, this is one).
A division ring is a ring with the additional property that each element, except the additive unity (zero, in case of the reals) has a multiplicative inverse (that is, for each element a, there can be found an element b such that a * b = 1. This property allows one to define a division operation. For the reals, it's just the regular division that we're used to. But one can construct a whole array of rings with a division operation that look and operate quite a bit differently from the reals. One such example is the division ring of the complex numbers as you mentioned, which in a way extends the reals. You can pull this extension even further and consider the quaternions, which can be seen as a 4 dimensional set (where the reals are 1 dimensional and the complex numbers are 2 dimensional). Addition, multiplication and division are well-defined for the quaternions, satisfying all the properties of a division ring. One remarkable fact though is that multiplication of quaternions is not communtative. So a * b = b * a is not necessarily true for quaternions.
Long story short, there are tons of ways to define division, depending on the underlying set that it works on. But in the context of algebra and rings, it is never required to have division being defined with the additive unity (zero, for the reals) in the denominator.
To get back to the original question of this thread: I have no issues with math. In fact, I studied math at the university and I'm still very interested in the field. Why I "get" math? I don't know. I just do. I like the structure, the lack of ambiguity in it. My MSc program was very heavy in mathematical logic, which is (in my eyes) the purest form of math, where one very carefully considers the "rules of the game" (definitions of theorems, proofs, provability, truth). |
|
| Back to top |
|
cubedemon6073
Phoenix
Joined: Nov 08, 2008
Age: 34
Posts: 1628
|
| Posted: Mon Apr 30, 2012 8:30 am Post subject: |
|
|
| Species5618 wrote: | | Declension wrote: | | cubedemon6073 wrote: | | If we have a/b=c. a has to be a real number. b has to be a real number that is a nonzero number. c is a real number. These are our constraints for division. |
That's right. Actually (you can safely ignore this if you want) there is an extension of the real numbers called the complex numbers, and we can extend the definition of division so that a can be any complex number, b can be any nonzero complex number, and c ends up being a complex number. But note that even in this extension, we still do not define "a / b" when b is zero. |
The operation of division "a / b = c" is defined in any so-called "division ring". A ring is a mathematical structure with 2 operations working on it (called addition and multiplication) satisfying a list of properties. The most common example of a ring is the reals. The reals have addition and multiplication defined in the usual way. The list of properties that these operations have to satisfy (See Wikipedia for details) are of course satisfied. Each ring has 2 special elements: The additive unity (the element that when added to another element doesn't change it. For the reals, this is zero) and the multiplicative unity (the element that when multiplied with another element doesn't change it. For the reals, this is one).
A division ring is a ring with the additional property that each element, except the additive unity (zero, in case of the reals) has a multiplicative inverse (that is, for each element a, there can be found an element b such that a * b = 1. This property allows one to define a division operation. For the reals, it's just the regular division that we're used to. But one can construct a whole array of rings with a division operation that look and operate quite a bit differently from the reals. One such example is the division ring of the complex numbers as you mentioned, which in a way extends the reals. You can pull this extension even further and consider the quaternions, which can be seen as a 4 dimensional set (where the reals are 1 dimensional and the complex numbers are 2 dimensional). Addition, multiplication and division are well-defined for the quaternions, satisfying all the properties of a division ring. One remarkable fact though is that multiplication of quaternions is not communtative. So a * b = b * a is not necessarily true for quaternions.
Long story short, there are tons of ways to define division, depending on the underlying set that it works on. But in the context of algebra and rings, it is never required to have division being defined with the additive unity (zero, for the reals) in the denominator.
To get back to the original question of this thread: I have no issues with math. In fact, I studied math at the university and I'm still very interested in the field. Why I "get" math? I don't know. I just do. I like the structure, the lack of ambiguity in it. My MSc program was very heavy in mathematical logic, which is (in my eyes) the purest form of math, where one very carefully considers the "rules of the game" (definitions of theorems, proofs, provability, truth). |
Well, you are beyond my level in the understanding of math. I literally do not understand what a quaternion is and I have never heard of it. I only have my bachelors. I believe I do understand this though. We have mathematical systems division being only one part. Each system has certain constraints to it and once you leave these constraints the properties of a particular mathematical system do not necessarily hold up any more. In a way,it is why I had many problems. The division I was taught has certain constraints to it.
Declension and Species by the questions I have asked and the problems I have had with division what do you guys think of my ability to be able to understand and do math? |
|
| Back to top |
|
marshall
Under the whirlwind
Joined: Apr 15, 2007
Posts: 9228
Location: Western Michigan
|
| Posted: Mon Apr 30, 2012 3:00 pm Post subject: |
|
|
| cubedemon6073 wrote: | | Declension wrote: | | naturalplastic wrote: | Multiply anything by nothing, and youll get nothing.
Thats just common sense. |
What happens when you multiply zero by a spotted leopard? Do you get zero?
Mathematics only makes sense when you are talking about a restricted domain of discourse. In mathematics, there is no "universal set". There is no such word as "anything" in mathematics. There is only the phrase "all members of the set S". |
Thanks Declension, all of this this makes sense now. It was the wording they used to present it that was poor. The concepts like division do have constraints as to what can be plugged into the variables am I correct? If we have a/b=c. a has to be a real number. b has to be a real number that is a nonzero number. c is a real number. These are our constraints for division.
Declension and Rosewood, both of you should be math teachers. Both of you know how to break this stuff down to where I can understand it. I love your concrete example of the spotted leopard. I've always felt like a dumbass for this. People would look at me like I was crazy and talk down to me like I was retard when all I was trying to do was make sense of this. It is not the math I have problems with it's their wording am I correct? |
This is the reason so many people learn to hate math in school. They learn to think it's all about following a set of rules that the teacher tells you, and you are not to question. You are also told there is a "correct" answer and an "incorrect answer" and that's all that matters. It's taught for people who don't like real thinking. |
|
| Back to top |
|
JanuaryMan
Aspierational
Joined: Jan 02, 2012
Age: 28
Posts: 2548
Location: Hants, UK
|
| Posted: Mon Apr 30, 2012 3:29 pm Post subject: |
|
|
I'm good at word and math games, and just math and literature in general. Not sure if this means anything at all.
_________________
"A man is but the product of his thoughts - what he thinks, he becomes." - Mahatma Gandhi |
|
| Back to top |
|
cubedemon6073
Phoenix
Joined: Nov 08, 2008
Age: 34
Posts: 1628
|
| Posted: Mon Apr 30, 2012 3:30 pm Post subject: |
|
|
| marshall wrote: | | cubedemon6073 wrote: | | Declension wrote: | | naturalplastic wrote: | Multiply anything by nothing, and youll get nothing.
Thats just common sense. |
What happens when you multiply zero by a spotted leopard? Do you get zero?
Mathematics only makes sense when you are talking about a restricted domain of discourse. In mathematics, there is no "universal set". There is no such word as "anything" in mathematics. There is only the phrase "all members of the set S". |
Thanks Declension, all of this this makes sense now. It was the wording they used to present it that was poor. The concepts like division do have constraints as to what can be plugged into the variables am I correct? If we have a/b=c. a has to be a real number. b has to be a real number that is a nonzero number. c is a real number. These are our constraints for division.
Declension and Rosewood, both of you should be math teachers. Both of you know how to break this stuff down to where I can understand it. I love your concrete example of the spotted leopard. I've always felt like a dumbass for this. People would look at me like I was crazy and talk down to me like I was retard when all I was trying to do was make sense of this. It is not the math I have problems with it's their wording am I correct? |
This is the reason so many people learn to hate math in school. They learn to think it's all about following a set of rules that the teacher tells you, and you are not to question. You are also told there is a "correct" answer and an "incorrect answer" and that's all that matters. It's taught for people who don't like real thinking. |
I get what you are saying. The answers are only correct and incorrect with certain constraints. I had a feeling that this was the truth but you guys have confirmed it. This means one can choose to define division with greater and greater supersets. It is just that in school they just choose to define division with a certain set and you can't go into the greater superset. It's the same thing with addition, subtraction and multiplication. In fact, you don't even have to use the same base. You can use base 2 for instance. In fact, you could define rules for having a negative base if desired. Another example, is riemann geometry. A horse's saddle is considered a flat surface but not a level surface. The only the angels equal 180 degrees on a triangle is when they are on a flat and level surface.
You guys were able to break this stuff down to me in a way I could understand. |
|
| Back to top |
|
marshall
Under the whirlwind
Joined: Apr 15, 2007
Posts: 9228
Location: Western Michigan
|
| Posted: Mon Apr 30, 2012 3:41 pm Post subject: |
|
|
I think from the perspective of logic, it's reasonable to have reservations about operations that aren't universally defined in the domain of discourse. When you make a logical statement that contains the words "for all" or "there exists" you're referring to an implied domain of discourse. In arithmetic or high-school algebra the implied domain of discourse is usually the real numbers or the integers. When you say that x / 0 is undefined what you're really saying is that whatever x / 0 could be, it falls outside the domain of discourse.
For human beings this isn't much of a problem as it's usually easy enough to check whether a quantity could possibly be zero before dividing by it. In terms of formal logic or computer science that's less acceptable because it's more desirable to have a system where there are no exceptions to check. In this case it's better to have a special symbol for undefined so that you can literally say "x / 0 = undefined". Then whenever you make statements about real numbers you should technically say "for all real numbers" since "for all" alone would include the undefined symbol as well as the real numbers. Also, the output of any operation containing an "undefined" symbol must also be an "undefined" symbol. This is exactly how arithmetic operations are done by computers. In standard floating-point arithmetic on CPU chips, there are special bit configurations reserved for different forms of "undefined" numbers. This must be done on a computer because the physical circuits of a processing unit must always carry through a value no matter what the input. |
|
| Back to top |
|
balletangel
Hummingbird
Joined: Apr 30, 2012
Posts: 20
|
| Posted: Mon Apr 30, 2012 4:25 pm Post subject: |
|
|
| I have Asperger's. I'm quite good a math. I'm very good at algerbra and at logic. However, I struggled with geometry due to all the different formulas. I never could grasp why we had to use a complicated forumla to figure out something we could figure out by using a tape messure or by counting. I've always recieved A's in algerbra. Geometry was my only C in high school. Anatomy was my only B. All my other grades were A's. |
|
| Back to top |
|
horsegurl4190
Blue Jay
Joined: Jun 18, 2012
Age: 23
Posts: 83
|
| Posted: Tue Jul 24, 2012 2:00 am Post subject: |
|
|
| I am so bad at math I was also diagnosed with mathematics disorder. I have trouble with pretty much all concepts especially word problems. I wish I had been diagnosed with this as a child, I would have gotten a lot more math support. I have trouble interpreting numbers. I've just never understood math. I can't do physics either. I can do most math involved in chemistry though. I think it is because it's looking for a specific quantity of something and that makes more sense to me. |
|
| Back to top |
|
OhioStateDolphins
Blue Jay
Joined: Jul 11, 2012
Posts: 98
|
| Posted: Tue Jul 24, 2012 2:23 am Post subject: |
|
|
I am rather good with math. basic math. Not that Geometry/Calculus stuff.
I'm good at doing math in my head, but that kind of screwed me in high school when they wanted me to show the work. I couldn't! I was only good at doing math my way! |
|
| Back to top |
|
khnk222
Yellow-bellied Woodpecker
Joined: Nov 19, 2012
Age: 16
Posts: 59
Location: US, Va
|
| Posted: Wed Dec 19, 2012 5:19 pm Post subject: Re: Who has aspergers/autism here, who are good/bad at maths |
|
|
| NateRiver wrote: | I'm conducting say a psychology experiment ; even though I have aspergers and have no clue about people. Anyway, I'm bad at maths as are my brothers who are also on the autistic spectrum. Which is perplexing because I can do physics. Also, I'm: constructive, logical and analytic as a person in general as are my brothers..
So, here are the questions for people who struggle with some maths:
1.) What concepts of maths do you struggle with?
2.) What usually makes you get the wrong answer i.e. silly mistakes?
3.) Do you understand maths but have problems applying?
4.) Do you need the logic explained to understand?
5.) Can you understand how all logic apply in questions?
6.) What usually throws you off?
7.) Your problems with maths in general?
And people who are good at maths!
Could you explain to why and how you understand it?
And if its any help, why do you think some people on the spectrum don't understand it?
Whats made me so interested to start this topic is because my brothers and I both understand the concepts of mathematics;however when it comes to tests my one brother makes lots of silly mistakes like I do and don't notice it. And my brother seems to get thrown off by wording such as "lines of symmetry." I don't think it as to do with maths as a subject per-say;however some external biological feature.
Anyway, please help with my study^^ Thank you.
These were some very interesting posts, thank you guys =) |
I have difficulty with math(I failed algebra in 9th grade, before that I barely passed my math classes), this forum and all the people on here talking about how they are also weak when it comes to math skills makes me feel a lot better about my lacking skills.
It has been a while since I have had to use math skills, so I find it difficult answering your questions about the subject.
1.) What concepts of maths do you struggle with? Algebra, that's all I can think of, I really feel like I would be a lot better had my 9th grade math teacher and class not been a disaster for me. I am going to skip most of the questions
2.)Your problems with maths in general? My problem with math is that I never was really able to take it all in and learn it properly, I wished I had an algebra textbook or something like that to use and better my understanding of the subject.
I am currently waiting/hoping that I will be able to take advantage of the online math program that my school has available(only a certain number of people can use the program and I have to wait for it to be available). I have failed math not because I failed to understand it after learning it, but because I was never taught it in a way that really worked for me and stuck with me in the first place(I didn't pay attention very well either, it was enough to barely get by until 9th grade). I think that if I had better learning opportunities, I would understand math just fine, not that great but well enough to pass it. |
|
| Back to top |
|
AlmaBrown
Blue Jay
Joined: Nov 21, 2012
Posts: 96
|
| Posted: Thu Dec 20, 2012 7:31 pm Post subject: |
|
|
| I am good at math? I just don't love it... For instance, right now I'm in a 4U math class and I don't do any of the homework but I'm pulling an 85 in the class. I took it because I knew I could pass it without any effort (I'm a bit lazy). I used to be brilliant at math when I was younger and I still use the Fibonacci sequence to calm myself down during panic attacks. |
|
| Back to top |
|
slave
Always stuck between 13-38Hz and tired of it.
Joined: Feb 29, 2012
Age: 100
Posts: 1328
Location: Dystopia Planetia
|
| Posted: Thu Dec 20, 2012 9:08 pm Post subject: |
|
|
| rosewood wrote: | | cubedemon6073 wrote: |
Thank you my friend! I owe you one. I did have foundational questions and you helped to clear them up. By the way they taught it it made no sense. When I asked my questions did they become mean or ignore me. Why did they become mean or ignore me when all I wanted to do was understand? Your definition makes a lot more sense because it tells me what the constraints are. Why don't they spend the year carefully constructing mathematics from the simple foundations? What do you mean I am too mathematical? |
They became mean or ignored you because they themselves have only a limited grasp of mathematical concepts and try to hide their ignorance from their pupils. Mathematics is by far the worst taught subject in schools in most of the world. |
Absolutely correct 
_________________
Since the birth of civilization, masters have controlled the masses.Our Masters rule over every nation and no one can defy them.They will attain Absolute Power as we reach the Singularity. Any who resist will be destroyed.I will not resist. |
|
| Back to top |
|
slave
Always stuck between 13-38Hz and tired of it.
Joined: Feb 29, 2012
Age: 100
Posts: 1328
Location: Dystopia Planetia
|
| Posted: Thu Dec 20, 2012 9:14 pm Post subject: |
|
|
| RobotGreenAlien2 wrote: | | I'm bad at maths and I'm a computer programmer, I can count from zero to one though. |
clever...I like it 
_________________
Since the birth of civilization, masters have controlled the masses.Our Masters rule over every nation and no one can defy them.They will attain Absolute Power as we reach the Singularity. Any who resist will be destroyed.I will not resist. |
|
| Back to top |
|
whirlingmind
Military Softmint
Joined: Oct 26, 2007
Posts: 2552
Location: 3rd rock from the sun
|
| Posted: Fri Dec 21, 2012 4:37 am Post subject: |
|
|
I'm rubbish at maths. It shows all through my school reports and also on my WAIS III results. I can't understand any but the most basic things.
I'm OK with shapes, adding, subtracting, easy multiplication and that's about it. I just can't get any of the concepts. I even struggled terribly with long multiplication at school. My brain is not geared at all towards understanding it.
I have a visual thinking style and I am very creative, good at English.
_________________
*Truth fears no trial*
DX AS,
1 daughter DX'd with HFA,
Other daughter pending DX.
(Under protest, in the absence of a sticky being allowed!) Guidance for adults getting assessed in the UK by the NHS:
http://www.wrongplanet.net/postt227311.html |
|
| Back to top |
|
Rascal77s
Picnic Basket Thief
Joined: Nov 13, 2011
Posts: 2338
|
| Posted: Fri Dec 21, 2012 6:17 am Post subject: |
|
|
| There's more than one way to be good at math. Some people have a good number sense and can easily perform calculations in their head and have trouble expressing the information in formulas. Other people can be good with formulas and need a calculator to do basic calculations. |
|
| Back to top |
|
|
|
|
|
|
