Superposition in math

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.
 

Ryan$

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thanks alot!!
 
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