0:00:00.012,0:00:04.212 In the past few minutes we've touched on a[br]lot of concepts that are going to play a 0:00:04.224,0:00:08.007 really central role in the rest of the[br]course and really in all math going 0:00:08.019,0:00:12.194 forwards from here. So I would like to do[br]a review of the algebra vocabulary that 0:00:12.206,0:00:16.046 we've covered so far. I think it's[br]actually going to amaze you how much we've 0:00:16.058,0:00:20.258 already gone over in a pretty short amount[br]of time. So first thing first, we have 0:00:20.270,0:00:24.800 numbers, as one might expect in math. So[br]what are some examples of numbers? Well, 0:00:24.898,0:00:29.215 we could have any number of things. So[br]like we learned in the very beginning of 0:00:29.227,0:00:33.738 this course, they're all different kinds[br]of numbers. Some that are pretty simple 0:00:33.750,0:00:38.253 and we use all the time, like 0 or 1 or[br]46, and some that are a little bit more 0:00:38.265,0:00:43.084 special, like the root of 2 or pi. Then in[br]contrast to numbers, we also learned about 0:00:43.096,0:00:48.125 variables. So, here we have all different[br]kinds of symbols, we have some letters, we 0:00:48.137,0:00:50.857 have some sillier things like hearts and[br]smiley faces, we got some greek letters. 0:00:51.285,0:00:55.919 But regardless of what we write variables[br]as they all have the same purpose, as we 0:00:55.931,0:01:00.528 learned earlier. Variables are symbols[br]that we use in equations and expressions 0:01:00.540,0:01:05.562 that serve as slots into which we can plug[br]other numbers to make our expressions take 0:01:05.574,0:01:09.959 on different values. So comparing numbers[br]and variables, numbers have fixed values. 0:01:10.053,0:01:14.413 They inherently show certain quantities.[br]Variables, however, don't show outright 0:01:14.425,0:01:18.721 what they stand for, they're just place[br]holders into which we can insert different 0:01:18.733,0:01:22.655 numbers. One thing to take note of when[br]we're looking at what's inside each of 0:01:22.667,0:01:27.479 these circles is that we actually have a[br]symbol on the number side. That's this pi 0:01:27.491,0:01:31.773 right here. Since pi is an irrational[br]number, it extends for an infinite number 0:01:31.785,0:01:35.822 of decimal points. Now, it took me an[br]awfully long time to write all of this 0:01:35.834,0:01:40.123 out. So if I were to write even more, that[br]would take me even longer. To make our 0:01:40.135,0:01:44.131 lives much more simple, we give this[br]infinitely long number a special name, 0:01:44.227,0:01:48.869 which is pi. A similar thing happens when[br]we write square roots. We have a number, 0:01:48.969,0:01:53.451 2, right here but we also have a square[br]root sign over it. Since the root of 2 is 0:01:53.463,0:01:57.858 also an irrational number the square root[br]sign is just another way of taking a 0:01:57.870,0:02:02.139 shortcut to not have to write out an[br]infinite number of decimals. So bottom 0:02:02.151,0:02:06.798 line, when you see symbols, they're almost[br]always variables. They'll be certain 0:02:06.810,0:02:11.783 cases. Which you'll become well acquainted[br]with when you see things like pi or like a 0:02:11.783,0:02:15.189 square root sign that are symbols of some[br]sort but represent numbers.