0:00:00.000,0:00:00.690 0:00:00.690,0:00:04.730 Most of us are familiar with[br]the equal sign from our earliest 0:00:04.730,0:00:06.330 days of arithmetic. 0:00:06.330,0:00:10.480 You might see something[br]like 1 plus 1 is equal to 2. 0:00:10.480,0:00:14.180 Now, a lot of people might[br]think when they see something 0:00:14.180,0:00:17.440 like this that somehow equal[br]means give me the answer. 0:00:17.440,0:00:19.100 1 plus 1 is the problem. 0:00:19.100,0:00:22.540 Equal means give me the[br]answer and 1 plus 1 is 2. 0:00:22.540,0:00:24.940 That's not what[br]equal actually means. 0:00:24.940,0:00:28.860 Equal is actually just trying[br]to compare two quantities. 0:00:28.860,0:00:32.250 When I write 1 plus 1[br]equals 2, that literally 0:00:32.250,0:00:34.640 means that what I[br]have on the left hand 0:00:34.640,0:00:39.370 side of the equal sign is the[br]exact same quantity as what 0:00:39.370,0:00:42.420 I have on the right hand[br]side of the equal sign. 0:00:42.420,0:00:48.990 I could have just as easily have[br]written 2 is equal to 1 plus 1. 0:00:48.990,0:00:50.950 These two things are equal. 0:00:50.950,0:00:54.250 I could have written[br]2 is equal to 2. 0:00:54.250,0:00:56.040 This is a completely[br]true statement. 0:00:56.040,0:00:57.500 These two things are equal. 0:00:57.500,0:01:02.970 I could have written 1 plus[br]1 is equal to 1 plus 1. 0:01:02.970,0:01:12.650 I could have written 1 plus 1[br]minus 1 is equal to 3 minus 2. 0:01:12.650,0:01:14.860 These are both equal quantities. 0:01:14.860,0:01:18.880 What I have here on[br]the left hand side, 0:01:18.880,0:01:23.680 this is 1 plus 1 minus 1 is 1[br]and this right over here is 1. 0:01:23.680,0:01:26.580 These are both equal quantities. 0:01:26.580,0:01:29.600 Now I will introduce[br]you to other ways 0:01:29.600,0:01:31.520 of comparing numbers. 0:01:31.520,0:01:34.760 The equal sign is when I[br]have the exact same quantity 0:01:34.760,0:01:35.805 on both sides. 0:01:35.805,0:01:37.180 Now we'll think[br]about what we can 0:01:37.180,0:01:40.430 do when we have different[br]quantities on both sides. 0:01:40.430,0:01:47.780 So let's say I have the number[br]3 and I have the number 1 0:01:47.780,0:01:50.140 and I want to compare them. 0:01:50.140,0:01:53.130 So clearly 3 and[br]1 are not equal. 0:01:53.130,0:01:54.630 In fact, I could[br]make that statement 0:01:54.630,0:01:56.080 with a not equal sign. 0:01:56.080,0:01:59.740 So I could say 3[br]does not equal 1. 0:01:59.740,0:02:02.410 But let's say I want to figure[br]out which one is a larger 0:02:02.410,0:02:03.860 and which one is smaller. 0:02:03.860,0:02:08.210 So if I want to have some[br]symbol where I can compare them, 0:02:08.210,0:02:12.900 where I can tell, where I can[br]state which of these is larger. 0:02:12.900,0:02:16.536 And the symbol for doing that[br]is the greater than symbol. 0:02:16.536,0:02:20.230 0:02:20.230,0:02:26.130 This literally would be[br]read as 3 is greater than 1. 0:02:26.130,0:02:28.450 3 is a larger quantity. 0:02:28.450,0:02:31.580 And if you have trouble[br]remembering what this means-- 0:02:31.580,0:02:36.105 greater than-- the larger[br]quantity is on the opening. 0:02:36.105,0:02:38.740 0:02:38.740,0:02:41.200 I guess if you could view[br]this as some type of an arrow, 0:02:41.200,0:02:45.370 or some type of symbol, but[br]this is the bigger side. 0:02:45.370,0:02:47.540 Here, you have this[br]little teeny, tiny point 0:02:47.540,0:02:49.895 and here you have the big[br]side, so the larger quantity 0:02:49.895,0:02:50.850 is on the big side. 0:02:50.850,0:02:52.860 This would literally[br]be read as 3 0:02:52.860,0:02:55.550 is greater than--[br]so let me write 0:02:55.550,0:03:02.420 that down-- greater than,[br]3 is greater than 1. 0:03:02.420,0:03:05.100 And once again, it just doesn't[br]have to be numbers like this. 0:03:05.100,0:03:06.470 I could write an expression. 0:03:06.470,0:03:18.130 I could write 1 plus 1 plus 1 is[br]greater than, let's say, well, 0:03:18.130,0:03:20.110 just one 1 right over there. 0:03:20.110,0:03:21.800 This is making a comparison. 0:03:21.800,0:03:23.910 But what if we had things[br]the other way around. 0:03:23.910,0:03:28.620 What if I wanted to make[br]a comparison between 5 0:03:28.620,0:03:33.040 and, let's say, 19. 0:03:33.040,0:03:35.500 So now the greater than[br]symbol wouldn't apply. 0:03:35.500,0:03:38.320 It's not true that 5[br]is greater than 19. 0:03:38.320,0:03:40.800 I could say that 5[br]is not equal to 19. 0:03:40.800,0:03:43.647 So I could still[br]make this statement. 0:03:43.647,0:03:45.980 But what if I wanted to make[br]a statement about which one 0:03:45.980,0:03:48.124 is larger and which[br]one is smaller? 0:03:48.124,0:03:49.540 Well, as in plain[br]English, I would 0:03:49.540,0:03:53.110 want to say 5 is less than 19. 0:03:53.110,0:03:55.720 So I would want to say--[br]let me write that down-- I 0:03:55.720,0:04:08.890 want to write 5 is less than 19. 0:04:08.890,0:04:10.189 That's what I want to say. 0:04:10.189,0:04:12.480 And so we just have to think[br]of a mathematical notation 0:04:12.480,0:04:16.769 for writing "is less than." 0:04:16.769,0:04:19.010 Well, if this is[br]greater than, it 0:04:19.010,0:04:21.329 makes complete sense that[br]let's just swap it around. 0:04:21.329,0:04:23.292 Let's make, once[br]again, the point 0:04:23.292,0:04:26.400 point towards the smaller[br]quantity and the big side 0:04:26.400,0:04:28.710 of the symbol point to[br]the larger quantity. 0:04:28.710,0:04:30.810 So here 5 is a smaller[br]quantity so I'll 0:04:30.810,0:04:32.390 make the point point there. 0:04:32.390,0:04:37.050 And 19 is a larger quantity,[br]so I'll make it open like this. 0:04:37.050,0:04:42.320 And so this would be read[br]as 5 is less than 19. 0:04:42.320,0:04:46.160 5 is a smaller quantity than 19. 0:04:46.160,0:04:52.700 I could also write this[br]as 1 plus 1 is less than 1 0:04:52.700,0:04:54.620 plus 1 plus 1. 0:04:54.620,0:04:56.830 It's just saying that this[br]statement, this quantity, 0:04:56.830,0:05:03.401 1 plus 1 is less[br]than 1 plus 1 plus 1. 0:05:03.401,0:05:03.901