[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.69,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.69,0:00:04.73,Default,,0000,0000,0000,,Most of us are familiar with\Nthe equal sign from our earliest
Dialogue: 0,0:00:04.73,0:00:06.33,Default,,0000,0000,0000,,days of arithmetic.
Dialogue: 0,0:00:06.33,0:00:10.48,Default,,0000,0000,0000,,You might see something\Nlike 1 plus 1 is equal to 2.
Dialogue: 0,0:00:10.48,0:00:14.18,Default,,0000,0000,0000,,Now, a lot of people might\Nthink when they see something
Dialogue: 0,0:00:14.18,0:00:17.44,Default,,0000,0000,0000,,like this that somehow equal\Nmeans give me the answer.
Dialogue: 0,0:00:17.44,0:00:19.10,Default,,0000,0000,0000,,1 plus 1 is the problem.
Dialogue: 0,0:00:19.10,0:00:22.54,Default,,0000,0000,0000,,Equal means give me the\Nanswer and 1 plus 1 is 2.
Dialogue: 0,0:00:22.54,0:00:24.94,Default,,0000,0000,0000,,That's not what\Nequal actually means.
Dialogue: 0,0:00:24.94,0:00:28.86,Default,,0000,0000,0000,,Equal is actually just trying\Nto compare two quantities.
Dialogue: 0,0:00:28.86,0:00:32.25,Default,,0000,0000,0000,,When I write 1 plus 1\Nequals 2, that literally
Dialogue: 0,0:00:32.25,0:00:34.64,Default,,0000,0000,0000,,means that what I\Nhave on the left hand
Dialogue: 0,0:00:34.64,0:00:39.37,Default,,0000,0000,0000,,side of the equal sign is the\Nexact same quantity as what
Dialogue: 0,0:00:39.37,0:00:42.42,Default,,0000,0000,0000,,I have on the right hand\Nside of the equal sign.
Dialogue: 0,0:00:42.42,0:00:48.99,Default,,0000,0000,0000,,I could have just as easily have\Nwritten 2 is equal to 1 plus 1.
Dialogue: 0,0:00:48.99,0:00:50.95,Default,,0000,0000,0000,,These two things are equal.
Dialogue: 0,0:00:50.95,0:00:54.25,Default,,0000,0000,0000,,I could have written\N2 is equal to 2.
Dialogue: 0,0:00:54.25,0:00:56.04,Default,,0000,0000,0000,,This is a completely\Ntrue statement.
Dialogue: 0,0:00:56.04,0:00:57.50,Default,,0000,0000,0000,,These two things are equal.
Dialogue: 0,0:00:57.50,0:01:02.97,Default,,0000,0000,0000,,I could have written 1 plus\N1 is equal to 1 plus 1.
Dialogue: 0,0:01:02.97,0:01:12.65,Default,,0000,0000,0000,,I could have written 1 plus 1\Nminus 1 is equal to 3 minus 2.
Dialogue: 0,0:01:12.65,0:01:14.86,Default,,0000,0000,0000,,These are both equal quantities.
Dialogue: 0,0:01:14.86,0:01:18.88,Default,,0000,0000,0000,,What I have here on\Nthe left hand side,
Dialogue: 0,0:01:18.88,0:01:23.68,Default,,0000,0000,0000,,this is 1 plus 1 minus 1 is 1\Nand this right over here is 1.
Dialogue: 0,0:01:23.68,0:01:26.58,Default,,0000,0000,0000,,These are both equal quantities.
Dialogue: 0,0:01:26.58,0:01:29.60,Default,,0000,0000,0000,,Now I will introduce\Nyou to other ways
Dialogue: 0,0:01:29.60,0:01:31.52,Default,,0000,0000,0000,,of comparing numbers.
Dialogue: 0,0:01:31.52,0:01:34.76,Default,,0000,0000,0000,,The equal sign is when I\Nhave the exact same quantity
Dialogue: 0,0:01:34.76,0:01:35.80,Default,,0000,0000,0000,,on both sides.
Dialogue: 0,0:01:35.80,0:01:37.18,Default,,0000,0000,0000,,Now we'll think\Nabout what we can
Dialogue: 0,0:01:37.18,0:01:40.43,Default,,0000,0000,0000,,do when we have different\Nquantities on both sides.
Dialogue: 0,0:01:40.43,0:01:47.78,Default,,0000,0000,0000,,So let's say I have the number\N3 and I have the number 1
Dialogue: 0,0:01:47.78,0:01:50.14,Default,,0000,0000,0000,,and I want to compare them.
Dialogue: 0,0:01:50.14,0:01:53.13,Default,,0000,0000,0000,,So clearly 3 and\N1 are not equal.
Dialogue: 0,0:01:53.13,0:01:54.63,Default,,0000,0000,0000,,In fact, I could\Nmake that statement
Dialogue: 0,0:01:54.63,0:01:56.08,Default,,0000,0000,0000,,with a not equal sign.
Dialogue: 0,0:01:56.08,0:01:59.74,Default,,0000,0000,0000,,So I could say 3\Ndoes not equal 1.
Dialogue: 0,0:01:59.74,0:02:02.41,Default,,0000,0000,0000,,But let's say I want to figure\Nout which one is a larger
Dialogue: 0,0:02:02.41,0:02:03.86,Default,,0000,0000,0000,,and which one is smaller.
Dialogue: 0,0:02:03.86,0:02:08.21,Default,,0000,0000,0000,,So if I want to have some\Nsymbol where I can compare them,
Dialogue: 0,0:02:08.21,0:02:12.90,Default,,0000,0000,0000,,where I can tell, where I can\Nstate which of these is larger.
Dialogue: 0,0:02:12.90,0:02:16.54,Default,,0000,0000,0000,,And the symbol for doing that\Nis the greater than symbol.
Dialogue: 0,0:02:16.54,0:02:20.23,Default,,0000,0000,0000,,
Dialogue: 0,0:02:20.23,0:02:26.13,Default,,0000,0000,0000,,This literally would be\Nread as 3 is greater than 1.
Dialogue: 0,0:02:26.13,0:02:28.45,Default,,0000,0000,0000,,3 is a larger quantity.
Dialogue: 0,0:02:28.45,0:02:31.58,Default,,0000,0000,0000,,And if you have trouble\Nremembering what this means--
Dialogue: 0,0:02:31.58,0:02:36.10,Default,,0000,0000,0000,,greater than-- the larger\Nquantity is on the opening.
Dialogue: 0,0:02:36.10,0:02:38.74,Default,,0000,0000,0000,,
Dialogue: 0,0:02:38.74,0:02:41.20,Default,,0000,0000,0000,,I guess if you could view\Nthis as some type of an arrow,
Dialogue: 0,0:02:41.20,0:02:45.37,Default,,0000,0000,0000,,or some type of symbol, but\Nthis is the bigger side.
Dialogue: 0,0:02:45.37,0:02:47.54,Default,,0000,0000,0000,,Here, you have this\Nlittle teeny, tiny point
Dialogue: 0,0:02:47.54,0:02:49.90,Default,,0000,0000,0000,,and here you have the big\Nside, so the larger quantity
Dialogue: 0,0:02:49.90,0:02:50.85,Default,,0000,0000,0000,,is on the big side.
Dialogue: 0,0:02:50.85,0:02:52.86,Default,,0000,0000,0000,,This would literally\Nbe read as 3
Dialogue: 0,0:02:52.86,0:02:55.55,Default,,0000,0000,0000,,is greater than--\Nso let me write
Dialogue: 0,0:02:55.55,0:03:02.42,Default,,0000,0000,0000,,that down-- greater than,\N3 is greater than 1.
Dialogue: 0,0:03:02.42,0:03:05.10,Default,,0000,0000,0000,,And once again, it just doesn't\Nhave to be numbers like this.
Dialogue: 0,0:03:05.10,0:03:06.47,Default,,0000,0000,0000,,I could write an expression.
Dialogue: 0,0:03:06.47,0:03:18.13,Default,,0000,0000,0000,,I could write 1 plus 1 plus 1 is\Ngreater than, let's say, well,
Dialogue: 0,0:03:18.13,0:03:20.11,Default,,0000,0000,0000,,just one 1 right over there.
Dialogue: 0,0:03:20.11,0:03:21.80,Default,,0000,0000,0000,,This is making a comparison.
Dialogue: 0,0:03:21.80,0:03:23.91,Default,,0000,0000,0000,,But what if we had things\Nthe other way around.
Dialogue: 0,0:03:23.91,0:03:28.62,Default,,0000,0000,0000,,What if I wanted to make\Na comparison between 5
Dialogue: 0,0:03:28.62,0:03:33.04,Default,,0000,0000,0000,,and, let's say, 19.
Dialogue: 0,0:03:33.04,0:03:35.50,Default,,0000,0000,0000,,So now the greater than\Nsymbol wouldn't apply.
Dialogue: 0,0:03:35.50,0:03:38.32,Default,,0000,0000,0000,,It's not true that 5\Nis greater than 19.
Dialogue: 0,0:03:38.32,0:03:40.80,Default,,0000,0000,0000,,I could say that 5\Nis not equal to 19.
Dialogue: 0,0:03:40.80,0:03:43.65,Default,,0000,0000,0000,,So I could still\Nmake this statement.
Dialogue: 0,0:03:43.65,0:03:45.98,Default,,0000,0000,0000,,But what if I wanted to make\Na statement about which one
Dialogue: 0,0:03:45.98,0:03:48.12,Default,,0000,0000,0000,,is larger and which\None is smaller?
Dialogue: 0,0:03:48.12,0:03:49.54,Default,,0000,0000,0000,,Well, as in plain\NEnglish, I would
Dialogue: 0,0:03:49.54,0:03:53.11,Default,,0000,0000,0000,,want to say 5 is less than 19.
Dialogue: 0,0:03:53.11,0:03:55.72,Default,,0000,0000,0000,,So I would want to say--\Nlet me write that down-- I
Dialogue: 0,0:03:55.72,0:04:08.89,Default,,0000,0000,0000,,want to write 5 is less than 19.
Dialogue: 0,0:04:08.89,0:04:10.19,Default,,0000,0000,0000,,That's what I want to say.
Dialogue: 0,0:04:10.19,0:04:12.48,Default,,0000,0000,0000,,And so we just have to think\Nof a mathematical notation
Dialogue: 0,0:04:12.48,0:04:16.77,Default,,0000,0000,0000,,for writing "is less than."
Dialogue: 0,0:04:16.77,0:04:19.01,Default,,0000,0000,0000,,Well, if this is\Ngreater than, it
Dialogue: 0,0:04:19.01,0:04:21.33,Default,,0000,0000,0000,,makes complete sense that\Nlet's just swap it around.
Dialogue: 0,0:04:21.33,0:04:23.29,Default,,0000,0000,0000,,Let's make, once\Nagain, the point
Dialogue: 0,0:04:23.29,0:04:26.40,Default,,0000,0000,0000,,point towards the smaller\Nquantity and the big side
Dialogue: 0,0:04:26.40,0:04:28.71,Default,,0000,0000,0000,,of the symbol point to\Nthe larger quantity.
Dialogue: 0,0:04:28.71,0:04:30.81,Default,,0000,0000,0000,,So here 5 is a smaller\Nquantity so I'll
Dialogue: 0,0:04:30.81,0:04:32.39,Default,,0000,0000,0000,,make the point point there.
Dialogue: 0,0:04:32.39,0:04:37.05,Default,,0000,0000,0000,,And 19 is a larger quantity,\Nso I'll make it open like this.
Dialogue: 0,0:04:37.05,0:04:42.32,Default,,0000,0000,0000,,And so this would be read\Nas 5 is less than 19.
Dialogue: 0,0:04:42.32,0:04:46.16,Default,,0000,0000,0000,,5 is a smaller quantity than 19.
Dialogue: 0,0:04:46.16,0:04:52.70,Default,,0000,0000,0000,,I could also write this\Nas 1 plus 1 is less than 1
Dialogue: 0,0:04:52.70,0:04:54.62,Default,,0000,0000,0000,,plus 1 plus 1.
Dialogue: 0,0:04:54.62,0:04:56.83,Default,,0000,0000,0000,,It's just saying that this\Nstatement, this quantity,
Dialogue: 0,0:04:56.83,0:05:03.40,Default,,0000,0000,0000,,1 plus 1 is less\Nthan 1 plus 1 plus 1.
Dialogue: 0,0:05:03.40,0:05:03.90,Default,,0000,0000,0000,,