Subtract quantities

Ryan$

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Hi guys, I'm so sorry to post like this thread but to understand me please I really am not trolling/joking ..whatever.
if I have an amount which is Composed from two things like object A and Object B, so lets assume the weight of that amount is 50, and given the weight of object A as 10, if I want to calculate the weight of object B then I do 50-10=40 and that's the weight of object B, my question is .. how do I imagine that subtraction? I mean I find it hard to analog that subtraction in my head on something more senseable in real life, is there any good analogy to imagine for subtraction amounts/adding quantities to each other?! how should I exactly imagine a quantity (NUMBER) in my head as what? if I succeed to imagine correctly what's the "quantity" then all the manipulation on it would be more easier .. so please help me as much as you guys can!


thanks
 

Ryan$

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to be more clear I imagine a subtraction of things/objects like this diagram .. but what's confusing me for instance if I do subtraction (A-(A&&B) ) then the left side of A excluded of (A&&B) will be the result of A-(A&&B) but what about the line between them isn't it having amount?! we must eliminate the line because we also subtract every point/line in the area of (A&&B) .. so here's my confusion .. the line is still although we subtract A&&B but the line between A and A&&B is still .. so it's weird and gets confused .. any help please?
 

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tkhunny

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Get a standard mass scale with pans on both ends. "Subtraction" happens by adding mass to the other side.
 

Dr.Peterson

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Don't think of the lines as part of the regions, but as fences separating them. You may even want to imagine that a disk has been cut into two parts which are just moved away from one another, so that the line is just empty space.

And keep in mind that pictures are just representations of ideas; you don't have to take everything literally.
 

Ryan$

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So if this is what you're saying, then how actually if I have lets assume problem then I can write it as collection of sub-problems which cover the whole problem itself ....... is it also a concept of ideas?
 

Dr.Peterson

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So if this is what you're saying, then how actually if I have lets assume problem then I can write it as collection of sub-problems which cover the whole problem itself ....... is it also a concept of ideas?
This is a totally separate question; it is not about subtracting quantities. But perhaps we can say that all of mathematics is about ideas, not about material realities themselves.

Please give a specific example of an actual problem that you want to "write as a collection of sub-problems", and ask a specific question about it, rather than keeping everything vague and unanswerable.
 

Ryan$

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if you say that all mathematics about ideas, what do you mean by that? just a concept of? nothing else no more?! thanks.
 

tkhunny

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"2" isn't much but some dots on a screen. Its importance is in what it represents.
 

Dr.Peterson

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if you say that all mathematics about ideas, what do you mean by that? just a concept of? nothing else no more?! thanks.
Math is the study of abstractions, which may be models of the real world (idealized lines and planes rather than things made of atoms, for example), or just "what if" thoughts about worlds that don't (as far as we know) exist physically.

When you draw a "circle", it is not really what we mean by a circle, because it has thickness and is not perfect. The picture represents an idea, which is what our math is about. If we apply it to a physical "circle", our conclusions will be only as accurate as the model.

When you add 2 and 3, you are not working with physical objects, but with a concept about them (which doesn't care what you are counting -- 2 sheep and 3 more sheep, or 2 miles and 3 more miles, or whatever).
 

Ryan$

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Math is the study of abstractions, which may be models of the real world (idealized lines and planes rather than things made of atoms, for example), or just "what if" thoughts about worlds that don't (as far as we know) exist physically.

When you draw a "circle", it is not really what we mean by a circle, because it has thickness and is not perfect. The picture represents an idea, which is what our math is about. If we apply it to a physical "circle", our conclusions will be only as accurate as the model.

When you add 2 and 3, you are not working with physical objects, but with a concept about them (which doesn't care what you are counting -- 2 sheep and 3 more sheep, or 2 miles and 3 more miles, or whatever).
You are proficient instructor ! thanks alot helped me very much more than you guess..
but I'm so curious as why I should follow those abstractions if its not exist or physically exist?
 

Dr.Peterson

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Two main reasons:
  • First, they tend to work! Mathematical models of reality give solutions that are good enough to be useful. For example, we can use a mathematical model of gravitation to get men to the moon.
  • Second, they are interesting! Just as we can enjoy fictional stories about nonexistent people or worlds, exercising our imagination, we can invent mathematical "worlds" just to see what happens, by making a definition and asking "what if" questions about it. (Sometimes the math we invent hypothetically turns out to describe something that hadn't been discovered yet, so this reason morphs into the other.)
 

HallsofIvy

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Think of it this way: Physics is the study of motion, force, energy, and the relations between them. Chemistry is about the study of elements, compounds, and the relations between them. Sociology is the study of people, groups of people, and the relations between them. Every discipline deals with certain "objects" and the relations between them.

Mathematics can be applied to all of those because mathematics is the study of "relationships" in the abstract.
 
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