need help understanding: if I have X then by superposition I can do X=x1+x2+x3+x4+x5+x6+x7+x8.....+xn

Ryan$

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Hi guys, I'm not getting the idea the superposition method in math, I mean if I have X then by superposition I can do X=x1+x2+x3+x4+x5+x6+x7+x8.....+xn
but why?! thanks. I'm not understanding the concept of superposition ..
 

JeffM

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Hi guys, I'm not getting the idea the superposition method in math, I mean if I have X then by superposition I can do X=x1+x2+x3+x4+x5+x6+x7+x8.....+xn
but why?! thanks. I'm not understanding the concept of superposition ..
I have no clue what you are talking about. You need to give a problem completely and exactly or, even better, give the definition of "superposition" used in your book.

What course did this come up in?

Are you by any chance talking about

\(\displaystyle \displaystyle X = \sum_{j=1}^n x_j.\)
 
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Ryan$

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Hi guys ! before making this thread I really thought multiple times for posting it or not but it's really something in my mind harassing me about what I'm going to ask.

What does quantity mean in math? why I'm asking about this because while I solving problems I always find obstacles about connections between quantities .. in other words for instance to find the value of something I may do sum of superposition on other things to find that value ! and doing that sum needs to understand what does quantity is !
 

Ryan$

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How should I imagine the quantity? I visualize it as something continues that's why I guess I found it a lil complex.

May anyone please instruct me how should I visualize/analog the quantity of something in math?
 

Jomo

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How should I imagine the quantity? I visualize it as something continues that's why I guess I found it a lil complex.

May anyone please instruct me how should I visualize/analog the quantity of something in math?
Quantity is how many you have. For example: I have 3-$5bills, I have 7 bananas, I owe you 3 oranges, I have 9x's etc...
 

Ryan$

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Quantity is how many you have. For example: I have 3-$5bills, I have 7 bananas, I owe you 3 oranges, I have 9x's etc...
Alright I'm with you, but once I start solving any problem in math specifically when there's something that equals a collections of other things then I start imagine that their "amounts" are related to each other and they are not separated (i.e words imagining the amounts as continues things) !


I will try to be more dramatically concrete about quantity term.


thanks you anyway mate!!
 

Jomo

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Alright I'm with you, but once I start solving any problem in math specifically when there's something that equals a collections of other things then I start imagine that their "amounts" are related to each other and they are not separated (i.e words imagining the amounts as continues things) !


I will try to be more dramatically concrete about quantity term.


thanks you anyway mate!!
You put amounts in quotation marks but are defining quantity. But that is OK.

something that equals a collections of other things then I start imagine that their "amounts" are related to each other and they are not separated.

I am not exactly sure what their means but I will try to address your concerns. I think by their you really mean to use a singular proverb not plural.

I guess you are thinking about something like x = $17.50y + $33z, where x is your total salary, y is the number of hours you worked at $17.50/hr and z is similarly defined. Yes, x is an amount! Its units are dollars. x IS relates to y and z. It is possible that y and z are separated but they are related to x. If you earn $17.50/hr and your mate earns $33/hr and your hours at work never cause any problems, then y and z are not related.
 

Ryan$

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You put amounts in quotation marks but are defining quantity. But that is OK.

something that equals a collections of other things then I start imagine that their "amounts" are related to each other and they are not separated.

I am not exactly sure what their means but I will try to address your concerns. I think by their you really mean to use a singular proverb not plural.

I guess you are thinking about something like x = $17.50y + $33z, where x is your total salary, y is the number of hours you worked at $17.50/hr and z is similarly defined. Yes, x is an amount! Its units are dollars. x IS relates to y and z. It is possible that y and z are separated but they are related to x. If you earn $17.50/hr and your mate earns $33/hr and your hours at work never cause any problems, then y and z are not related.
VERY meaningful!! helped me alot thanks!!!

another thing in the same concept, lets assume a pressure of something is defined as quantity ; so sometimes in order to find a pressure of specific thing we should do superposition of other things ! and this trick doesn't ring in my mind always ... so I guess it doesn't ring always because I miss the concept of the term "superposition". ( I mean with superposition like this X=x1+x2+x3+x4+x5+x6 )

if you clear up the term superposition by analogous to be remembered in my mind and thank you in advance.
 

Subhotosh Khan

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VERY meaningful!! helped me alot thanks!!!

another thing in the same concept, lets assume a pressure of something is defined as quantity ; so sometimes

in order to find a pressure of specific thing we should do superposition of other things !

and this trick doesn't ring in my mind always ... so I guess it doesn't ring always because I miss the concept of the term "superposition". ( I mean with superposition like this X=x1+x2+x3+x4+x5+x6 )

if you clear up the term superposition by analogous to be remembered in my mind and thank you in advance.
Can you please provide an example of this phenomenon?
 

Jomo

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Can you please provide an example of this phenomenon?
Please note that this is at least the 2nd time we asked this student to define/give an example of superposition.
 

Ryan$

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Can you please provide an example of this phenomenon?
Yes sorry for not clearing it out.

lets assume I have 7 potatoes which each of them weight 1kl , then if x is the total weight and xi the the weight of one potato ,
so the total weight = sum of all xi that I've i.e X=x1+x2+x3+...+x7 (that's called superposition)
 

Ryan$

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Please note that this is at least the 2nd time we asked this student to define/give an example of superposition.
I didn't notice before.
 

Ryan$

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Hi guys, in brief , By superposition I can implicitly manage all of the problems, I mean I can always look at problem in its general regardless of +/-/* arithmetic math manipulation, what's confusing me is, how do I remember that always?! I mean lets assume I have one orange+one orange=two orange , but "two orange" by superposition I can say it's also generally orange .. so anyone can help me how should I visualize the superposition of things among things? it's like something magic that convert all the collection to one specific thing with the same type of the elements of the collections ..


thanks
 

tkhunny

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That's not even a question.

Why not ponder multiplication? one orange * one orange = ?? Is THAT still "generally orange"? Does it even exist?
Are you talking about linear systems?
Are you talking about quantum systems in multiple, simultaneous states?
Are you talking about photo-superposition in photography?
Are you talking about a new layer of substrate in a geological structure?

Why would you EXPECT to be able to "visualize the superposition of things among things"? That is FAR to vague for any such expectation.

Distinct objects may be related. Does it have ANYTHING to do with "superposition"? Is that the same thing as simply grouping?
 

Otis

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Your English is like water vapor, to me. I know something is there; I just can't see it.

Can you post a link to what you're looking at, so people can see it?
 

Ryan$

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to be more direct and sorry for my light English writing, lets assume you have X is integer and Y is integer, so we are considering also X+Y is integer in general, I mean the component X+Y also integer although it has "+" in its term ..so my question how it's integer? like wise in analogy of X [type of something] + Y[type of something] I can relate to the term "X+Y" also as [Type of something] but why I can relate to the term although it has + between X and Y as a [Type of something] ? thanks.
 

Otis

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to be more direct … X is integer and Y is integer …

… [consider] X+Y is integer …

… so my question how it's integer? …
X+Y is an Integer because the set of Integers is closed under addition.
 

Ryan$

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what do you mean by "is closed under addition " ?!
 

tkhunny

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Closed Under Addition: Add things and don't get something else.

Integer + Integer ==> Integer -- Closed
Integer / Integer ==> Might be an Integer, Might be a Rational Number, might not exist. -- Not Closed
Orange + Orange ==> Orange -- They don't magically turn into Soursops. -- Closed
 

Otis

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what do you mean by "is closed under addition" ?!
A set is "closed under addition" if adding any elements in the set results in another element in the set.

If you add Integers together, you are guaranteed to get another Integer.

We can have closure with other operations, too. The set of Integers is closed under addition, subtraction, multiplication and exponentiation.

Another example: The set of positive Integers is closed under addition but not subtraction.

1 - 2 = -1

Subtraction with two elements of the set yielded an element that is not in the set.
 
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