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### Sets and Subsets

```
Date: 23 Jan 1995 14:45:14 -0500
From: Xin Li
Subject: Sets and Subsets

In my algebra 1 class, my teacher talked about sets and subsets.
You might wonder why I asked problems about SIN and COS and now
I'm back on the basics.  Well, I learn from two math books.  One
covers that kind of stuff and another covers the basics.  I'm
teaches me stuff on that book while I have to keep up with work
from my math class.  Anyway, my teacher talks about Sets and
Subsets. She said that integers are a subset of reals, and whole
numbers are a subset of integers, and counting numbers are a
subset of whole numbers, and so on and so forth.  What does that
mean?  I'm having a test on that tomorrow, so if you could help
me to get this info down today, I'll be forever grateful.

Thanks.
```

```
Date: 23 Jan 1995 21:51:38 -0500
From: Dr. Sydney
Subject: Re: Sets and Subsets

Dear Xin,

When we say a set (let's call it A) is a subset of another
subset (let's call it B), that means that every element that is
in A is also in B.  For instance, the counting numbers (this is
the set: {1, 2, 3, ...}) is a subset of the whole numbers (this
is the set {0, 1, 2,...}, I think!). This is because every
element in the set of counting numbers is also in the set of
whole numbers.  1, 2, 3, ... are all whole numbers.  Does that
make sense?

Similarly the whole numbers are a subset of the integers because
every element of the set of whole numbers is also in the set of
integers (that is the set {...-2, -1, 0, 1, 2, ...}).  Do you
see?

I hope this helps. Write back if you have any more questions.

--Sydney, dr. math
```

```
Date: 24 Jan 1995 17:27:54 -0500
From: Xin Li
Subject: Sets and Subsets

Yeah, I think I get it now.  Suppose we say in bag A, there are
10 apples and in bag B there are 10 apples and 10 oranges, then
we could say that bag A is a subset of bag B because bag B has
everything bag A has.  Is that what it means?
```

```
Date: 24 Jan 1995 18:09:31 -0500
From: Dr. Sydney
(Sydney Foster)
Subject: Re: Sets and Subsets

Dear Xin,

Yes, that is it!  Good example.  If you have any other problems,
write us back!

--Sydney, Dr. Math

From: Dr. Steve
(Steve Weimar)
Subject: Sets and Subsets

Dear Xin,

It looks as though you do have the idea, although it might be more accurate
to imagine that bag A has ten apples and in bag B there are ten oranges AND
bag A. Then the fruit in bag A could be described as a subset of the fruit
in bag B.

-- Dr. Steve
```
Associated Topics:
High School Basic Algebra
High School Sets
Middle School Algebra

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