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Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.01,0:00:04.21,Default,,0000,0000,0000,,In the past few minutes we've touched on a\Nlot of concepts that are going to play a
Dialogue: 0,0:00:04.22,0:00:08.01,Default,,0000,0000,0000,,really central role in the rest of the\Ncourse and really in all math going
Dialogue: 0,0:00:08.02,0:00:12.19,Default,,0000,0000,0000,,forwards from here. So I would like to do\Na review of the algebra vocabulary that
Dialogue: 0,0:00:12.21,0:00:16.05,Default,,0000,0000,0000,,we've covered so far. I think it's\Nactually going to amaze you how much we've
Dialogue: 0,0:00:16.06,0:00:20.26,Default,,0000,0000,0000,,already gone over in a pretty short amount\Nof time. So first thing first, we have
Dialogue: 0,0:00:20.27,0:00:24.80,Default,,0000,0000,0000,,numbers, as one might expect in math. So\Nwhat are some examples of numbers? Well,
Dialogue: 0,0:00:24.90,0:00:29.22,Default,,0000,0000,0000,,we could have any number of things. So\Nlike we learned in the very beginning of
Dialogue: 0,0:00:29.23,0:00:33.74,Default,,0000,0000,0000,,this course, they're all different kinds\Nof numbers. Some that are pretty simple
Dialogue: 0,0:00:33.75,0:00:38.25,Default,,0000,0000,0000,,and we use all the time, like 0 or 1 or\N46, and some that are a little bit more
Dialogue: 0,0:00:38.26,0:00:43.08,Default,,0000,0000,0000,,special, like the root of 2 or pi. Then in\Ncontrast to numbers, we also learned about
Dialogue: 0,0:00:43.10,0:00:48.12,Default,,0000,0000,0000,,variables. So, here we have all different\Nkinds of symbols, we have some letters, we
Dialogue: 0,0:00:48.14,0:00:50.86,Default,,0000,0000,0000,,have some sillier things like hearts and\Nsmiley faces, we got some greek letters.
Dialogue: 0,0:00:51.28,0:00:55.92,Default,,0000,0000,0000,,But regardless of what we write variables\Nas they all have the same purpose, as we
Dialogue: 0,0:00:55.93,0:01:00.53,Default,,0000,0000,0000,,learned earlier. Variables are symbols\Nthat we use in equations and expressions
Dialogue: 0,0:01:00.54,0:01:05.56,Default,,0000,0000,0000,,that serve as slots into which we can plug\Nother numbers to make our expressions take
Dialogue: 0,0:01:05.57,0:01:09.96,Default,,0000,0000,0000,,on different values. So comparing numbers\Nand variables, numbers have fixed values.
Dialogue: 0,0:01:10.05,0:01:14.41,Default,,0000,0000,0000,,They inherently show certain quantities.\NVariables, however, don't show outright
Dialogue: 0,0:01:14.42,0:01:18.72,Default,,0000,0000,0000,,what they stand for, they're just place\Nholders into which we can insert different
Dialogue: 0,0:01:18.73,0:01:22.66,Default,,0000,0000,0000,,numbers. One thing to take note of when\Nwe're looking at what's inside each of
Dialogue: 0,0:01:22.67,0:01:27.48,Default,,0000,0000,0000,,these circles is that we actually have a\Nsymbol on the number side. That's this pi
Dialogue: 0,0:01:27.49,0:01:31.77,Default,,0000,0000,0000,,right here. Since pi is an irrational\Nnumber, it extends for an infinite number
Dialogue: 0,0:01:31.78,0:01:35.82,Default,,0000,0000,0000,,of decimal points. Now, it took me an\Nawfully long time to write all of this
Dialogue: 0,0:01:35.83,0:01:40.12,Default,,0000,0000,0000,,out. So if I were to write even more, that\Nwould take me even longer. To make our
Dialogue: 0,0:01:40.14,0:01:44.13,Default,,0000,0000,0000,,lives much more simple, we give this\Ninfinitely long number a special name,
Dialogue: 0,0:01:44.23,0:01:48.87,Default,,0000,0000,0000,,which is pi. A similar thing happens when\Nwe write square roots. We have a number,
Dialogue: 0,0:01:48.97,0:01:53.45,Default,,0000,0000,0000,,2, right here but we also have a square\Nroot sign over it. Since the root of 2 is
Dialogue: 0,0:01:53.46,0:01:57.86,Default,,0000,0000,0000,,also an irrational number the square root\Nsign is just another way of taking a
Dialogue: 0,0:01:57.87,0:02:02.14,Default,,0000,0000,0000,,shortcut to not have to write out an\Ninfinite number of decimals. So bottom
Dialogue: 0,0:02:02.15,0:02:06.80,Default,,0000,0000,0000,,line, when you see symbols, they're almost\Nalways variables. They'll be certain
Dialogue: 0,0:02:06.81,0:02:11.78,Default,,0000,0000,0000,,cases. Which you'll become well acquainted\Nwith when you see things like pi or like a
Dialogue: 0,0:02:11.78,0:02:15.19,Default,,0000,0000,0000,,square root sign that are symbols of some\Nsort but represent numbers.