# Subtract quantities

##### Junior Member
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

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

#### Dr.Peterson

##### Elite Member
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.

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

#### tkhunny

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

#### Dr.Peterson

##### Elite Member
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\$

##### Junior Member
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

##### Elite Member
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

##### Elite Member
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.