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Most of us are familiar with
the equal sign from our earliest

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days of arithmetic.

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You might see something
like 1 plus 1 is equal to 2.

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Now, a lot of people might
think when they see something

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like this that somehow equal
means give me the answer.

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1 plus 1 is the problem.

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Equal means give me the
answer and 1 plus 1 is 2.

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That's not what
equal actually means.

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Equal is actually just trying
to compare two quantities.

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When I write 1 plus 1
equals 2, that literally

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means that what I
have on the left hand

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side of the equal sign is the
exact same quantity as what

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I have on the right hand
side of the equal sign.

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I could have just as easily have
written 2 is equal to 1 plus 1.

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These two things are equal.

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I could have written
2 is equal to 2.

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This is a completely
true statement.

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These two things are equal.

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I could have written 1 plus
1 is equal to 1 plus 1.

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I could have written 1 plus 1
minus 1 is equal to 3 minus 2.

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These are both equal quantities.

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What I have here on
the left hand side,

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this is 1 plus 1 minus 1 is 1
and this right over here is 1.

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These are both equal quantities.

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Now I will introduce
you to other ways

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of comparing numbers.

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The equal sign is when I
have the exact same quantity

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on both sides.

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Now we'll think
about what we can

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do when we have different
quantities on both sides.

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So let's say I have the number
3 and I have the number 1

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and I want to compare them.

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So clearly 3 and
1 are not equal.

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In fact, I could
make that statement

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with a not equal sign.

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So I could say 3
does not equal 1.

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But let's say I want to figure
out which one is a larger

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and which one is smaller.

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So if I want to have some
symbol where I can compare them,

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where I can tell, where I can
state which of these is larger.

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And the symbol for doing that
is the greater than symbol.

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This literally would be
read as 3 is greater than 1.

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3 is a larger quantity.

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And if you have trouble
remembering what this means--

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greater than-- the larger
quantity is on the opening.

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I guess if you could view
this as some type of an arrow,

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or some type of symbol, but
this is the bigger side.

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Here, you have this
little teeny, tiny point

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and here you have the big
side, so the larger quantity

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is on the big side.

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This would literally
be read as 3

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is greater than--
so let me write

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that down-- greater than,
3 is greater than 1.

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And once again, it just doesn't
have to be numbers like this.

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I could write an expression.

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I could write 1 plus 1 plus 1 is
greater than, let's say, well,

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just one 1 right over there.

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This is making a comparison.

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But what if we had things
the other way around.

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What if I wanted to make
a comparison between 5

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and, let's say, 19.

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So now the greater than
symbol wouldn't apply.

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It's not true that 5
is greater than 19.

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I could say that 5
is not equal to 19.

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So I could still
make this statement.

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But what if I wanted to make
a statement about which one

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is larger and which
one is smaller?

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Well, as in plain
English, I would

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want to say 5 is less than 19.

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So I would want to say--
let me write that down-- I

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want to write 5 is less than 19.

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That's what I want to say.

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And so we just have to think
of a mathematical notation

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for writing "is less than."

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Well, if this is
greater than, it

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makes complete sense that
let's just swap it around.

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Let's make, once
again, the point

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point towards the smaller
quantity and the big side

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of the symbol point to
the larger quantity.

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So here 5 is a smaller
quantity so I'll

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make the point point there.

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And 19 is a larger quantity,
so I'll make it open like this.

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And so this would be read
as 5 is less than 19.

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5 is a smaller quantity than 19.

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I could also write this
as 1 plus 1 is less than 1

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plus 1 plus 1.

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It's just saying that this
statement, this quantity,

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1 plus 1 is less
than 1 plus 1 plus 1.

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