In the past few minutes we've touched on a
lot of concepts that are going to play a
really central role in the rest of the
course and really in all math going
forwards from here. So I would like to do
a review of the algebra vocabulary that
we've covered so far. I think it's
actually going to amaze you how much we've
already gone over in a pretty short amount
of time. So first thing first, we have
numbers, as one might expect in math. So
what are some examples of numbers? Well,
we could have any number of things. So
like we learned in the very beginning of
this course, they're all different kinds
of numbers. Some that are pretty simple
and we use all the time, like 0 or 1 or
46, and some that are a little bit more
special, like the root of 2 or pi. Then in
contrast to numbers, we also learned about
variables. So, here we have all different
kinds of symbols, we have some letters, we
have some sillier things like hearts and
smiley faces, we got some greek letters.
But regardless of what we write variables
as they all have the same purpose, as we
learned earlier. Variables are symbols
that we use in equations and expressions
that serve as slots into which we can plug
other numbers to make our expressions take
on different values. So comparing numbers
and variables, numbers have fixed values.
They inherently show certain quantities.
Variables, however, don't show outright
what they stand for, they're just place
holders into which we can insert different
numbers. One thing to take note of when
we're looking at what's inside each of
these circles is that we actually have a
symbol on the number side. That's this pi
right here. Since pi is an irrational
number, it extends for an infinite number
of decimal points. Now, it took me an
awfully long time to write all of this
out. So if I were to write even more, that
would take me even longer. To make our
lives much more simple, we give this
infinitely long number a special name,
which is pi. A similar thing happens when
we write square roots. We have a number,
2, right here but we also have a square
root sign over it. Since the root of 2 is
also an irrational number the square root
sign is just another way of taking a
shortcut to not have to write out an
infinite number of decimals. So bottom
line, when you see symbols, they're almost
always variables. They'll be certain
cases. Which you'll become well acquainted
with when you see things like pi or like a
square root sign that are symbols of some
sort but represent numbers.