Greater than and less than symbols

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

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

Now a lot of people might think when they
see

something like this that somehow equal
means give me the answer.

1 plus 1 is a problem, equal means give me
the answer, and 1 plus 1 is two.

That's not what equal actually means.

Equal is actually just trying to compare
two quantities.

When I write 1 plus 1 equals 2, that
literally

means, that what I have on the left hand
side

of the equal sign, is the exact same
quantity as

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

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

These two things are equal.

I could have written 2 is equal to 2.

This is a completely true statement, these
two things are equal.

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

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

These are both equal quantities.

What I have here on the left hand side,
this is, this is 1, 1 plus 1 minus

1 is 1, and this right over here is 1,
these are both equal quantities.

Now, I will introduce you to other ways of
comparing numbers.

These are, the equal sign is when I have
the exact same quantity on both sides.

Now we'll think about what we can do

when we have different quantities on both
sides.

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

I have the number 1, and I wanna compare
them.

So clearly, 3 and 1 are not equal, in fact
I

can make that statement with a not equal
sign, so I

can say 3 does not equal 1, but let's say
I

wanna figure out which one is larger and
which one is smaller.

So, if I wanna have some symbol, where I
can compare them, where

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

And the symbol for doing that is

the greater than symbol, the greater than
symbol.

This literally would be read as 3 is
greater than 1, 3 is a larger quantity.

And if you need, if you have trouble
remembering what this, that this

means greater than, the larger quantity,
the

larger quantities on the opening, the
larger

on the, the, the larger, I guess if you
could view this as some

type of an arrow or, I guess a shet, well,
some type of symbol.

Then this is the bigger side.

Here you have this little teeny tiny
point, and here you

have the big side so the larger quantity's
on the big side.

This would literally be read as 3 is
greater than, so let me write that down.

Greater than, 3 is greater than 1.

And once again, it just doesn't have to

be numbers like this, I could write an
expression.

I could write, I could write 1 plus 1 plus
1, is greater than,

is greater than, let's say, well just one
1 right over there.

This is making a comparison.

But what if we had things the other way
around?

What if I wanted to make a comparison
between 5, and let's say 19.

So now the greater than symbol wouldn't
apply,

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

I could say that 5 is not equal to 19,

so I could still make, I could still make
this

statement, but what if I wanted to make a
statement

about which one is larger and which one is
smaller?

Well if in plain English, I would wanna
say 5

is less than 19, so I would wanna say, let

me write that down, I wanna write 5 is
less

than, 5 is, is less than is less than 19.

That's what I wanna say, and so we just
have to think

of a mathematical notation for writing is,
for writing is less than.

Well if this is greater than it makes
complete

sense, and let's just swap it around,
let's make, once

again, the point point towards the smaller
quantity and the

big side of the symbol point to the larger
quantity.

So here 5 is a smaller quantity, so I'll
make the point point

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

And so this would be read as 5 is less
than 19, 5 is a smaller quantity than 19.

I could also write this as, I could write
1 plus 1 is less that 1 plus 1 plus 1.

It's just saying that this statement, this
quantity, 1

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