point in math

To be more exact !
once I solve a question, the concept of using a coordination system is ring on my head, but immediately I ask my self why I can use it?!! here I can't answer myself so I stuck!!!!
 
I think this has been said repeatedly: \(\text{You, Tom, D}\text{ick}\) and \(\text{Harry}\) may well choose different axes to solve some problem, arriving at very different values for "x", "y", and "z". But those values are NOT the solutions to the problem. The solution process consists of using those values and your definitions of "x", "y", and "z" (in terms of the original problem) to answer whatever questions the problem asked.
 
To build on what several others have said. You describe triangle ABC as having point A at (0, 0), point B at (0,4), and point C at (3, 0). I describe triangle ABC as having point A at (-2, -5), point B at (-2, -1), and point C (1, -5). They are different names to describe the same triangle.

The relations specified are the same. You will calculate the length of AB as 4. I shall calculate the length of AB as -1 - (-5) = 4. You will calculate the length of AC as 3. I shall calculate the length of AC as 1 - (-2) = 3. So both of us will calculate the length of BC as 5. In other words, the relations between A, B, and C are the same no matter what coordinate system you choose.

Mark asked you to work through a specific problem using different coordinate systems. In most cases, you would have found that the choice did not matter because it is an issue of names, not fundamentals. Because you framed this in the abstract without reference to a specific problem, you made the incorrect assumption that it would matter and so asked a foolish question.

Halls mentioned another point. If different coordinate systems appear to give different numerical results, it is because the different coordinate systems are measuring different things. Again, this would be clear if you gave a specific example.
 
Ryan$ said:
but once again you're talking with who don't have master in math, why I may orient a system of coordinate as I see?! maybe someone sees it different .. so ?! .. in math I can "define" whatever I want?!
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We know that you are not a "master" in math. However you have asked a basic question here and, on a beginner's level, that you should take the view that maybe we know what we are talking about and you should try to simply apply it. For any problem you are likely to run into you can choose whatever set of axes you like. So please go with the assumption we know what we are talking about and apply it. You won't need the reason for it for quite some time in the future.

-Dan
 
HallsofIvy said:
A coordinate system is something we impose upon a problem. For example, suppose we have a problem in which we are told that a rock is thrown upward, at 2 m/s, from a 200 m tall building. If I want to use y''= -g, I can set up a coordinate system in which y= 0 at the bottom of the building and have initial conditions y(0)= 500, y'(0)= 2. Or I could set up a coordinate system in which y= 0 at the top of the building and y= 200 at the bottom. Then we would have to use y''= g (since "+" is downward) with initial conditions y(0)= 0, y'(0)= -2.

Yes, solving those different problems gives different solutions for y (the first gives y(t)= -(g/2)t^2- 2t+ 500 and the second y(t)= -(g/2)t^2- 2t but interpreted in terms of the coordinate system, they give the same solution. In particular, if the question is "when does the rock hit the bottom, using the first "coordinate system" we need to solve the equation -(g/2)t^2- 2t+ 500= 0 and in the second, (g/2)t^2+ 2t= 500. Those two equations have exactly the same solution.
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HoI, That is an excellent explanation.

However, Jason "pretends" not to understand "linear problems" like Lev used in response #9 - I don't see any hope that he would understand (or even try to understand) the example given by you.
 
Hi guys! Yes it maybe easy for others but it's really hard me and I need to grasp the concept so please burden me !

if I have : 5---------------6-------------7 which "---------" is straight line , if I want the distance between 5 and 6 then I do 6-5 =1 but now if I want the distance between 6 and 7 then I do 7-6-epsilon because we already calculated the point of 6 in the distance between 6-5 .. but in math is telling me that distance between 7 and 6 is 7-6 without epsilon .. I mean without - epsilon, what's going on exactly? why we are considering the point 6 twice in distance between 5-6 and between 6-7 ? it really makes it hard for me ..I need to grasp the concept ..how the theoretical concepts define the idea of " point "?! thanks alot !
I claim if we calculated the point of 6 in distance 6-5 because we calculated the amount of distance between 6-5 , then we must wipe the point of 6 off in calculating the distance between 6-7 ! and that's because we already calculated the point of 6 in distance between 5-6 .. but apparently I'm wrong .. I don't know why any help?! maybe I define a point in a wrong way?! how math define point ?
 
Subtraction works. There is no epsilon.

"Point" is axiomatic. No definition needed. No need to grasp at it.

7-6 has nothing to do with 6-5.
 
Ryan$ said:
if I have : 5---------------6-------------7 which "---------" is straight line , if I want the distance between 5 and 6 then I do 6-5 =1 but now if I want the distance between 6 and 7 then I do 7-6-epsilon because we already calculated the point of 6 in the distance between 6-5 .. but in math is telling me
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There is a simple reason there you do not understand: You are just too hardheaded to learn the basics. These postulates have been studied sense the late 1980's first set by one of the greatest mathematicians to ever have lived, David Hilbert. The ruler postulate states that Every line had a coordinate system. That means if \(\displaystyle \ell\) is a line there exists a bijective function \(\displaystyle f:\ell \leftrightarrow R\). There are a whole set of metric requirements for coordinate systems. With which we can say that if \(\displaystyle \{P~\&~Q\}\subset \ell\) the distance \(\displaystyle \delta(P,Q)=|f(P)-f(Q)|\).
Please don't show you own ignorance by stating patently false accusations.
 
Hi guys !
just I'm wondering , if we multiply 4[chairs] by 3, which I do 3*4[chair] but what's the unit of 3? I mean if it's unitless then how we multiply unitless with unit of chairs? don't make sense .... any help to understand why 3*4[chairs] will give 12[chair] ? I dont mean why it's 12 .. but how we are allowed to multiply two things without same unit ?!!!

is [unitless]*[unit]=[unit] ..doesn't make sense .. may anyone explain that for me ?! all what confusing me is we are doing multiplying to different units ..
 
"3" is just counting how many groups of chairs. Then the "4" is NOT "4 chairs" but "4 chairs per group" (or "4 chairs/group) so that this is "(3 groups)(4 chairs/group)= 12 chairs, the "groups" cancelling.

"How are we allowed to multiply two things without the same unit?"
We do that all the time! There is no requirement that "two things have the same unit" when we multiply or divide. If a car gets 24
"miles/gallon" and there are 8 gallons of gas in its tank then the car can go (24 miles/gallon)(8 gallons)= 188 miles. Conversely we get "miles/gallon" by dividing the miles the car has gone by the number of gallons of gas required.

If we add or subtract quantities they must have the same units- but not if we multiply or divide.
 
There is no rule prohibiting this. Math doesn't care about your units. You can include units in your calculations to make sure the resulting units make sense. In this case they do. Where do you see a problem? Do you expect the result to be something other than chairs?
 
Are you realy confused whether you have 12 chairs if you have 4 chairs in the den of your house, 4 chairs in the living room, and 4 chairs in the dining room? Do you suspect that if you put all of them in the hall, you will count 12 lizards?

Math stems from an idealization of the processes of counting and measuring things physically, not from deep contemplation of dimensional analysis.

Now as HOI points out, dimensional analysis in this case IS PERFECTLY consistent with the facts of common experience. You just did the dimensional analysis wrong.

[MATH]3 \text { groups of chairs} \times \dfrac{4 \text { chairs}}{\text {group}} = 12 \text { chairs.}[/MATH]
In your calculation, 3 was not unitless in terms of dimensional analysis. So you asked a remarkably inane question.
 
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Hi guys!
I've a question that's given all its inputs(information) in cm
and while solving the question I needed to use an formula that's just allowing me to use Unit in Meters (assume that)
then what's confusing me is:
the given information is in cm, and I in a problem that in order to use the formula I need unit in meters , so how math solve that semi-problem?
if you tell me to convert cm(given information in cm) to meters, but then you are changing the given information and that's not allowed?!
any help how can I overcome on that problem? I need really a good explanation

thanks alot
 
Ryan$ said:
Hi guys!
I've a question that's given all its inputs(information) in cm
and while solving the question I needed to use an formula that's just allowing me to use Unit in Meters (assume that)
then what's confusing me is:
the given information is in cm, and I in a problem that in order to use the formula I need unit in meters , so how math solve that semi-problem?
if you tell me to convert cm(given information in cm) to meters, but then you are changing the given information and that's not allowed?!
any help how can I overcome on that problem? I need really a good explanation

thanks alot
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Where is the problem statement?
 
You have already posted this question. 1 m = 100 cm. The two are equivalent. What about this are you (still) not understanding?

I also think that it would be best to post in the original thread if you still don't understand it.

(Moderator Note: Duplicated threads merged)

-Dan
 
BAN THIS TROLL.

I must admit, however, I would prefer if people would say

[MATH]x \text { meters} = 100x \text { centimeters}[/MATH]
so that fools like Ryan will understand that the 100 to 1 equivalence between centimeters and meters is general and applies to more than the isolated case of 100 centimeters.
 
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Hi guys, here I opened a thread about point and answered me that point doesn't have any volume /value /whatever
then in differential like df(x)/dt then because it's differential then it works for points .. so here points have a value .. but we already discussed that points don't have value .. so it's opposite to what math has defined .. ? any help please? win the definition of "differential" , it works for point !
 
The derivative is a function, not a point. To get the math behind it, you need to study standard or non-standard analysis.

Given that you do not understand arithmetic, you are not going to grasp analysis in either form..
 
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