[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.36,0:00:07.73,Default,,0000,0000,0000,,Mathematics has its own\Nlanguage, most of which which
Dialogue: 0,0:00:07.73,0:00:14.10,Default,,0000,0000,0000,,were very familiar with. For\Nexample, the digits 012.
Dialogue: 0,0:00:14.12,0:00:21.59,Default,,0000,0000,0000,,345678 and nine are part\Nof our everyday lives, and
Dialogue: 0,0:00:21.59,0:00:27.57,Default,,0000,0000,0000,,whether we refer to this\Ndigit as zero.
Dialogue: 0,0:00:28.10,0:00:31.04,Default,,0000,0000,0000,,Nothing.
Dialogue: 0,0:00:31.57,0:00:38.04,Default,,0000,0000,0000,,Note\NOh oh, as in the
Dialogue: 0,0:00:38.04,0:00:42.35,Default,,0000,0000,0000,,telephone code 0191 we\Nunderstand its meaning.
Dialogue: 0,0:00:43.65,0:00:47.78,Default,,0000,0000,0000,,There are many symbols in\Nmathematics and most of them are
Dialogue: 0,0:00:47.78,0:00:50.02,Default,,0000,0000,0000,,used as a precise form of
Dialogue: 0,0:00:50.02,0:00:54.96,Default,,0000,0000,0000,,shorthand. We need to be\Nconfident using the symbols and
Dialogue: 0,0:00:54.96,0:00:59.14,Default,,0000,0000,0000,,to gain that confidence, we need\Nto understand their meaning.
Dialogue: 0,0:01:00.46,0:01:06.58,Default,,0000,0000,0000,,To understand that meaning,\Nwe've got two things to help us,
Dialogue: 0,0:01:06.58,0:01:11.95,Default,,0000,0000,0000,,there's context. What else is\Nwith the symbol? What's with it?
Dialogue: 0,0:01:11.95,0:01:13.84,Default,,0000,0000,0000,,What's it all about?
Dialogue: 0,0:01:14.69,0:01:19.18,Default,,0000,0000,0000,,And this convention and\Nconvention is where
Dialogue: 0,0:01:19.18,0:01:23.04,Default,,0000,0000,0000,,Mathematicians and\Nscientists have decided that
Dialogue: 0,0:01:23.04,0:01:26.89,Default,,0000,0000,0000,,particular symbols will\Nrepresent particular things.
Dialogue: 0,0:01:28.34,0:01:29.85,Default,,0000,0000,0000,,Let's have a look at some
Dialogue: 0,0:01:29.85,0:01:36.67,Default,,0000,0000,0000,,symbols. That sign words\Nassociated with it
Dialogue: 0,0:01:36.67,0:01:39.25,Default,,0000,0000,0000,,a plus. That
Dialogue: 0,0:01:40.26,0:01:43.58,Default,,0000,0000,0000,,Increase.
Dialogue: 0,0:01:44.43,0:01:51.09,Default,,0000,0000,0000,,And positive. As\Nit stands, it has some form of
Dialogue: 0,0:01:51.09,0:01:56.96,Default,,0000,0000,0000,,meaning, but we really need it\Nin a context. For example, 2 + 3
Dialogue: 0,0:01:56.96,0:02:02.40,Default,,0000,0000,0000,,or two ad three. We know the\Ncontext, we add the two numbers
Dialogue: 0,0:02:02.40,0:02:04.08,Default,,0000,0000,0000,,and we get 5.
Dialogue: 0,0:02:05.30,0:02:10.17,Default,,0000,0000,0000,,Let's have a look at another\Ncontext. Now, if you've gone
Dialogue: 0,0:02:10.17,0:02:15.49,Default,,0000,0000,0000,,abroad, say to Europe, and you'd\Ngone to a conference, you might
Dialogue: 0,0:02:15.49,0:02:20.36,Default,,0000,0000,0000,,hand out some business cards,\Nand on your business card so
Dialogue: 0,0:02:20.36,0:02:24.79,Default,,0000,0000,0000,,that people could contact you.\NYou might have your telephone
Dialogue: 0,0:02:24.79,0:02:30.55,Default,,0000,0000,0000,,number, so chances are it will\Nbe written as plus 44, and let's
Dialogue: 0,0:02:30.55,0:02:32.77,Default,,0000,0000,0000,,have a phone number 1911234567.
Dialogue: 0,0:02:33.93,0:02:40.89,Default,,0000,0000,0000,,And in this context, that plus\Nmeans that the person dials the
Dialogue: 0,0:02:40.89,0:02:45.53,Default,,0000,0000,0000,,necessary code for an\Ninternational line from their
Dialogue: 0,0:02:45.53,0:02:47.27,Default,,0000,0000,0000,,country, then 441911234567.
Dialogue: 0,0:02:47.92,0:02:53.00,Default,,0000,0000,0000,,So it still means In addition\Nto, but not in the same way as
Dialogue: 0,0:02:53.00,0:02:56.100,Default,,0000,0000,0000,,that plus sign were not actually\Nadding the number on. We're
Dialogue: 0,0:02:56.100,0:02:58.45,Default,,0000,0000,0000,,doing it In addition.
Dialogue: 0,0:03:00.00,0:03:03.87,Default,,0000,0000,0000,,Let's have a look
Dialogue: 0,0:03:03.87,0:03:08.42,Default,,0000,0000,0000,,now. At this\Nsign.
Dialogue: 0,0:03:09.63,0:03:14.99,Default,,0000,0000,0000,,Well, it's associated with this\None and minus.
Dialogue: 0,0:03:14.99,0:03:18.96,Default,,0000,0000,0000,,Subtract. Take
Dialogue: 0,0:03:18.96,0:03:20.43,Default,,0000,0000,0000,,away.
Dialogue: 0,0:03:20.43,0:03:23.76,Default,,0000,0000,0000,,Negative.
Dialogue: 0,0:03:23.76,0:03:30.79,Default,,0000,0000,0000,,And decrease.\NAnd again, we need a context.
Dialogue: 0,0:03:30.79,0:03:36.08,Default,,0000,0000,0000,,Let's six takeaway four or six.\NSubtract 4 and we all know the
Dialogue: 0,0:03:36.08,0:03:37.71,Default,,0000,0000,0000,,answer to be 2.
Dialogue: 0,0:03:38.29,0:03:43.68,Default,,0000,0000,0000,,In a different context, if we\Nhave minus 5 degrees C for
Dialogue: 0,0:03:43.68,0:03:48.14,Default,,0000,0000,0000,,example. That means a\Ntemperature of five
Dialogue: 0,0:03:48.14,0:03:49.75,Default,,0000,0000,0000,,degrees below 0.
Dialogue: 0,0:03:51.49,0:03:54.41,Default,,0000,0000,0000,,How about this one?
Dialogue: 0,0:03:54.96,0:04:02.15,Default,,0000,0000,0000,,Words associated with\Nthis symbol multiply.
Dialogue: 0,0:04:02.15,0:04:09.34,Default,,0000,0000,0000,,Lots of. Times Now\Nthis one is really just a
Dialogue: 0,0:04:09.34,0:04:11.10,Default,,0000,0000,0000,,shorthand for adding.
Dialogue: 0,0:04:12.12,0:04:17.06,Default,,0000,0000,0000,,Let's have a look at the\Ncontext. For example, six at 6,
Dialogue: 0,0:04:17.06,0:04:19.54,Default,,0000,0000,0000,,at 6, at 6 at 6.
Dialogue: 0,0:04:20.39,0:04:24.01,Default,,0000,0000,0000,,What we've actually got a
Dialogue: 0,0:04:24.01,0:04:31.08,Default,,0000,0000,0000,,123456 is. And in short\Nhand we want to write 5 sixes.
Dialogue: 0,0:04:31.80,0:04:36.60,Default,,0000,0000,0000,,On the symbol that's used is the\Nmultiply sign, so we've got five
Dialogue: 0,0:04:36.60,0:04:39.18,Default,,0000,0000,0000,,lots of 6 or 5 * 6.
Dialogue: 0,0:04:40.72,0:04:45.03,Default,,0000,0000,0000,,Now this shorthand becomes even\Nshorter when we use some letters
Dialogue: 0,0:04:45.03,0:04:46.21,Default,,0000,0000,0000,,instead of numbers.
Dialogue: 0,0:04:46.93,0:04:53.90,Default,,0000,0000,0000,,So for example, instead of six,\Nlet's say we were adding AA
Dialogue: 0,0:04:53.90,0:04:56.81,Default,,0000,0000,0000,,again, will have 5 days.
Dialogue: 0,0:04:57.99,0:05:02.68,Default,,0000,0000,0000,,But because we've used the\Nletter, if we use the multiply.
Dialogue: 0,0:05:03.21,0:05:06.59,Default,,0000,0000,0000,,It could be confused\Nwith the letter X.
Dialogue: 0,0:05:08.12,0:05:12.81,Default,,0000,0000,0000,,So we don't write it in.\NBasically we miss it out and we
Dialogue: 0,0:05:12.81,0:05:16.42,Default,,0000,0000,0000,,just write 5, eh? So the\Nshorthand becomes shorter, so
Dialogue: 0,0:05:16.42,0:05:20.39,Default,,0000,0000,0000,,when letters are involved, the\Nmultiply sign is missed out is
Dialogue: 0,0:05:20.39,0:05:22.56,Default,,0000,0000,0000,,the only symbol that we miss
Dialogue: 0,0:05:22.56,0:05:28.36,Default,,0000,0000,0000,,out. Let's look\Nat division.
Dialogue: 0,0:05:29.96,0:05:34.46,Default,,0000,0000,0000,,Now this symbol can actually be\Nwritten in three different ways.
Dialogue: 0,0:05:34.61,0:05:37.41,Default,,0000,0000,0000,,We could have 10 / 5.
Dialogue: 0,0:05:38.17,0:05:44.82,Default,,0000,0000,0000,,10 / 5 as it's written in a\Nfraction or 10 with a slash
Dialogue: 0,0:05:44.82,0:05:49.57,Default,,0000,0000,0000,,and five now this ones come\Nabout mainly because of
Dialogue: 0,0:05:49.57,0:05:53.84,Default,,0000,0000,0000,,printing and typing and using\Na computer. When these
Dialogue: 0,0:05:53.84,0:05:57.64,Default,,0000,0000,0000,,symbols are not readily\Navailable on the keyboard.
Dialogue: 0,0:05:58.78,0:06:05.60,Default,,0000,0000,0000,,So how many times does 5 go\Ninto 10 or 10 / 5?
Dialogue: 0,0:06:06.92,0:06:11.73,Default,,0000,0000,0000,,Another very common symbol that\Nwe use all the time without
Dialogue: 0,0:06:11.73,0:06:13.91,Default,,0000,0000,0000,,thinking is the equals sign.
Dialogue: 0,0:06:14.82,0:06:19.93,Default,,0000,0000,0000,,Again, it doesn't mean anything\Non its own. We need it in some
Dialogue: 0,0:06:19.93,0:06:25.43,Default,,0000,0000,0000,,form of context. So if we have\Nthe sum 1 + 2 equals 3.
Dialogue: 0,0:06:26.01,0:06:32.35,Default,,0000,0000,0000,,What we're saying is whatever we\Nhave on this side is exactly
Dialogue: 0,0:06:32.35,0:06:35.00,Default,,0000,0000,0000,,equal to. Whatever we have on
Dialogue: 0,0:06:35.00,0:06:38.98,Default,,0000,0000,0000,,this side. Or it's the same as?
Dialogue: 0,0:06:39.96,0:06:43.19,Default,,0000,0000,0000,,Variations on the
Dialogue: 0,0:06:43.19,0:06:49.83,Default,,0000,0000,0000,,equals sign. Of the\Nnot equal sign, a line through
Dialogue: 0,0:06:49.83,0:06:52.77,Default,,0000,0000,0000,,the equals which is not equal
Dialogue: 0,0:06:52.77,0:06:58.46,Default,,0000,0000,0000,,to. For example, X is not\Nequal to two.
Dialogue: 0,0:06:59.26,0:07:02.48,Default,,0000,0000,0000,,So we know that X does not take\Nthat value of two.
Dialogue: 0,0:07:03.56,0:07:09.55,Default,,0000,0000,0000,,Two WAVY lines without\Nequals means approximately
Dialogue: 0,0:07:09.55,0:07:11.26,Default,,0000,0000,0000,,equal to.
Dialogue: 0,0:07:12.29,0:07:18.63,Default,,0000,0000,0000,,So it may not be\Nexact, but it's approximately
Dialogue: 0,0:07:18.63,0:07:21.44,Default,,0000,0000,0000,,equal to that value.
Dialogue: 0,0:07:23.23,0:07:28.02,Default,,0000,0000,0000,,Are greater than\Nor equal sign?
Dialogue: 0,0:07:29.06,0:07:36.21,Default,,0000,0000,0000,,An example here\Nmight be X
Dialogue: 0,0:07:36.21,0:07:43.35,Default,,0000,0000,0000,,is greater than\Nor equal to
Dialogue: 0,0:07:43.35,0:07:49.42,Default,,0000,0000,0000,,two. That means X could take the\Nvalue of two, but it could be
Dialogue: 0,0:07:49.42,0:07:50.100,Default,,0000,0000,0000,,any number larger than two.
Dialogue: 0,0:07:52.53,0:07:56.44,Default,,0000,0000,0000,,And are less
Dialogue: 0,0:07:56.44,0:08:01.13,Default,,0000,0000,0000,,than. Or equal\N2.
Dialogue: 0,0:08:02.27,0:08:08.76,Default,,0000,0000,0000,,I'm here for example. Why would\Nbe less than or equal to 7?
Dialogue: 0,0:08:09.53,0:08:13.99,Default,,0000,0000,0000,,Why could equals 7? But it could\Nbe any number less than 7.
Dialogue: 0,0:08:14.92,0:08:18.87,Default,,0000,0000,0000,,And an easy way of remembering\Nwhich is the greater and the
Dialogue: 0,0:08:18.87,0:08:22.82,Default,,0000,0000,0000,,less than part is the greater\Nis the wider part of the
Dialogue: 0,0:08:22.82,0:08:25.78,Default,,0000,0000,0000,,symbol, whatever's on the\Nwider part of the symbol,
Dialogue: 0,0:08:25.78,0:08:29.72,Default,,0000,0000,0000,,whatever's on that side is the\Ngreater than the one where the
Dialogue: 0,0:08:29.72,0:08:31.70,Default,,0000,0000,0000,,point is on the other side.
Dialogue: 0,0:08:33.60,0:08:39.54,Default,,0000,0000,0000,,Other forms\Nof mathematical
Dialogue: 0,0:08:39.54,0:08:42.50,Default,,0000,0000,0000,,symbols are
Dialogue: 0,0:08:42.50,0:08:49.26,Default,,0000,0000,0000,,variables. I'm\Nbasing used where things
Dialogue: 0,0:08:49.26,0:08:51.94,Default,,0000,0000,0000,,take different values.
Dialogue: 0,0:08:52.71,0:08:56.10,Default,,0000,0000,0000,,For example, imagine your\Njourney to work in your car.
Dialogue: 0,0:08:56.67,0:09:01.56,Default,,0000,0000,0000,,And imagine the speed that\Nyou're traveling at as you go
Dialogue: 0,0:09:01.56,0:09:05.57,Default,,0000,0000,0000,,along your journey, your\Nspeed will change, so we
Dialogue: 0,0:09:05.57,0:09:10.46,Default,,0000,0000,0000,,might refer to the speed with\Na letter. Let's say the
Dialogue: 0,0:09:10.46,0:09:14.02,Default,,0000,0000,0000,,letter V, because throughout\Nyour journey the actual
Dialogue: 0,0:09:14.02,0:09:15.80,Default,,0000,0000,0000,,numerical value is changing.
Dialogue: 0,0:09:18.00,0:09:21.31,Default,,0000,0000,0000,,We usually use letters for\Nvariables, letters of the
Dialogue: 0,0:09:21.31,0:09:23.15,Default,,0000,0000,0000,,alphabet. You can call them
Dialogue: 0,0:09:23.15,0:09:28.30,Default,,0000,0000,0000,,anything. But we try to use\Nletters of the alphabet and we
Dialogue: 0,0:09:28.30,0:09:32.92,Default,,0000,0000,0000,,try to have those letters giving\Nus some indication of what our
Dialogue: 0,0:09:32.92,0:09:34.46,Default,,0000,0000,0000,,variable is all about.
Dialogue: 0,0:09:35.37,0:09:40.87,Default,,0000,0000,0000,,For example, we might use\Ndeep for distance.
Dialogue: 0,0:09:41.80,0:09:44.83,Default,,0000,0000,0000,,And T for time.
Dialogue: 0,0:09:48.31,0:09:54.02,Default,,0000,0000,0000,,By convention, we use you to\Nbe initial speed.
Dialogue: 0,0:09:54.80,0:10:01.05,Default,,0000,0000,0000,,And V to\Nbe our final
Dialogue: 0,0:10:01.05,0:10:07.90,Default,,0000,0000,0000,,speed. But of course, we\Nmight also refer to volume.
Dialogue: 0,0:10:08.77,0:10:13.46,Default,,0000,0000,0000,,And This is why context is\Nimportant and we look to see
Dialogue: 0,0:10:13.46,0:10:18.54,Default,,0000,0000,0000,,what a variable is with as to\Nwhat it might mean. So, for
Dialogue: 0,0:10:18.54,0:10:22.85,Default,,0000,0000,0000,,example, if we were to CV is D\Ndivided by T.
Dialogue: 0,0:10:24.24,0:10:29.38,Default,,0000,0000,0000,,And we're told that Diaz\Ndistance and T is time. Then we
Dialogue: 0,0:10:29.38,0:10:31.94,Default,,0000,0000,0000,,know that that V is speed.
Dialogue: 0,0:10:33.47,0:10:40.64,Default,,0000,0000,0000,,Whereas if we saw V\Nwith Four Thirds Paillard cubed.
Dialogue: 0,0:10:41.18,0:10:47.75,Default,,0000,0000,0000,,Where are is the radius of a\Nsphere. We know that that V is
Dialogue: 0,0:10:47.75,0:10:50.56,Default,,0000,0000,0000,,also the volume of a sphere.
Dialogue: 0,0:10:51.73,0:10:56.44,Default,,0000,0000,0000,,Now going back to our example\Nagain of our journey to work, we
Dialogue: 0,0:10:56.44,0:11:01.87,Default,,0000,0000,0000,,might want to record the time it\Ntook us to go to work, and we
Dialogue: 0,0:11:01.87,0:11:05.49,Default,,0000,0000,0000,,might want to do that over a\Nnumber of days.
Dialogue: 0,0:11:06.90,0:11:11.58,Default,,0000,0000,0000,,The most sensible variable to\Nuse would be a T for our time.
Dialogue: 0,0:11:12.29,0:11:16.38,Default,,0000,0000,0000,,But of course, if we want to\Nrecord it for each day, how do
Dialogue: 0,0:11:16.38,0:11:17.84,Default,,0000,0000,0000,,we distinguish between the TS?
Dialogue: 0,0:11:18.53,0:11:23.98,Default,,0000,0000,0000,,Well, in this case we\Nuse a subscript.
Dialogue: 0,0:11:23.98,0:11:27.77,Default,,0000,0000,0000,,So for day
Dialogue: 0,0:11:27.77,0:11:31.23,Default,,0000,0000,0000,,one. We might
Dialogue: 0,0:11:31.23,0:11:38.28,Default,,0000,0000,0000,,use T1. The\Nnext day to
Dialogue: 0,0:11:38.28,0:11:45.27,Default,,0000,0000,0000,,223-2425. Or we might want\Nto be a little bit clearer and
Dialogue: 0,0:11:45.27,0:11:50.68,Default,,0000,0000,0000,,actually put perhaps TM for the\Ntime on Monday TT for Tuesday
Dialogue: 0,0:11:50.68,0:11:56.55,Default,,0000,0000,0000,,TW. For Wednesday we would have\Nto do TH for Thursday so it
Dialogue: 0,0:11:56.55,0:12:01.51,Default,,0000,0000,0000,,doesn't get confused with\NTuesday and TF for Friday, so we
Dialogue: 0,0:12:01.51,0:12:06.47,Default,,0000,0000,0000,,can use these subscripts small\Nnumbers or letters at the bottom
Dialogue: 0,0:12:06.47,0:12:10.08,Default,,0000,0000,0000,,right of the variable to\Ndistinguish between them.
Dialogue: 0,0:12:11.15,0:12:16.37,Default,,0000,0000,0000,,Now, by convention,\Nmathematicians have decided that
Dialogue: 0,0:12:16.37,0:12:23.83,Default,,0000,0000,0000,,we're going to use some\Nletters of the Greek alphabet
Dialogue: 0,0:12:23.83,0:12:27.56,Default,,0000,0000,0000,,for some of our mathematical
Dialogue: 0,0:12:27.56,0:12:33.21,Default,,0000,0000,0000,,symbols. For example,\Nwe have pie.
Dialogue: 0,0:12:33.98,0:12:40.84,Default,,0000,0000,0000,,Empires being chosen to equal\Nthe number 3.14159 and it
Dialogue: 0,0:12:40.84,0:12:46.33,Default,,0000,0000,0000,,goes on and on forever,\Nnever repeats itself.
Dialogue: 0,0:12:47.25,0:12:53.07,Default,,0000,0000,0000,,And so that we can precisely say\Nwhat we mean, rather than having
Dialogue: 0,0:12:53.07,0:12:54.87,Default,,0000,0000,0000,,to round the value.
Dialogue: 0,0:12:55.43,0:12:59.73,Default,,0000,0000,0000,,We use the letter Pi knowing\Nthat it's that number.
Dialogue: 0,0:13:01.12,0:13:07.44,Default,,0000,0000,0000,,From the Greek alphabet we also\Nuse some other letters such as
Dialogue: 0,0:13:07.44,0:13:10.58,Default,,0000,0000,0000,,Alpha. 's
Dialogue: 0,0:13:10.58,0:13:14.30,Default,,0000,0000,0000,,pizza. And
Dialogue: 0,0:13:14.30,0:13:21.68,Default,,0000,0000,0000,,feature. Now, these\Nare often used as variables to
Dialogue: 0,0:13:21.68,0:13:27.88,Default,,0000,0000,0000,,represent angles. So you might\Nsee an angle marked in that way,
Dialogue: 0,0:13:27.88,0:13:29.97,Default,,0000,0000,0000,,and the Greek letter Theta.
Dialogue: 0,0:13:31.47,0:13:36.76,Default,,0000,0000,0000,,Another one that is commonly\Nused is a capital Sigma.
Dialogue: 0,0:13:37.58,0:13:41.99,Default,,0000,0000,0000,,Now you should be familiar with\Nthis one from any spreadsheet
Dialogue: 0,0:13:41.99,0:13:46.40,Default,,0000,0000,0000,,program on a computer, because\Nyou'll find it somewhere on the
Dialogue: 0,0:13:46.40,0:13:48.81,Default,,0000,0000,0000,,toolbar because it means the sum
Dialogue: 0,0:13:48.81,0:13:55.63,Default,,0000,0000,0000,,of. And it's a shorthand for\Nadding up a column or a row of
Dialogue: 0,0:13:55.63,0:14:00.03,Default,,0000,0000,0000,,numbers on a spreadsheet. So it\Nmeans the sum of.
Dialogue: 0,0:14:01.88,0:14:06.35,Default,,0000,0000,0000,,The positioning of where we put\Nletters or figures without
Dialogue: 0,0:14:06.35,0:14:13.35,Default,,0000,0000,0000,,symbols. Has gives meaning to\Nit, just like our subscripts we
Dialogue: 0,0:14:13.35,0:14:15.75,Default,,0000,0000,0000,,can have superscripts now
Dialogue: 0,0:14:15.75,0:14:20.26,Default,,0000,0000,0000,,superscripts. Instead of going\Nat the bottom right, go at the
Dialogue: 0,0:14:20.26,0:14:24.99,Default,,0000,0000,0000,,top right. So for example, for\Nthe little two at the top right
Dialogue: 0,0:14:24.99,0:14:26.81,Default,,0000,0000,0000,,hand side, that's a superscript.
Dialogue: 0,0:14:27.60,0:14:33.92,Default,,0000,0000,0000,,And again, it's a shorthand as\Nmost of our symbols are and that
Dialogue: 0,0:14:33.92,0:14:35.38,Default,,0000,0000,0000,,means 4 squared.
Dialogue: 0,0:14:35.91,0:14:40.05,Default,,0000,0000,0000,,4 *\N4.
Dialogue: 0,0:14:41.84,0:14:44.63,Default,,0000,0000,0000,,If we have 4 cubed.
Dialogue: 0,0:14:45.15,0:14:52.57,Default,,0000,0000,0000,,We've got three of them,\N4 * 4 * 4.
Dialogue: 0,0:14:53.23,0:14:57.76,Default,,0000,0000,0000,,Alright, a number that means to\Nthe power of.
Dialogue: 0,0:15:00.19,0:15:07.26,Default,,0000,0000,0000,,So we've raised 4 to the power\Nof three 4 * 4 * 4.
Dialogue: 0,0:15:08.93,0:15:13.13,Default,,0000,0000,0000,,32
Dialogue: 0,0:15:14.27,0:15:19.17,Default,,0000,0000,0000,,With the 0 as a superscript now\Nthis is actually got two
Dialogue: 0,0:15:19.17,0:15:23.46,Default,,0000,0000,0000,,meanings. And we need the\Ncontext to be able to know which
Dialogue: 0,0:15:23.46,0:15:29.69,Default,,0000,0000,0000,,meaning it is. It could\Nbe 32 degrees.
Dialogue: 0,0:15:30.54,0:15:33.59,Default,,0000,0000,0000,,And that would mean an angle.
Dialogue: 0,0:15:34.14,0:15:35.89,Default,,0000,0000,0000,,Of 32 degrees.
Dialogue: 0,0:15:37.46,0:15:40.79,Default,,0000,0000,0000,,But it could mean 32.
Dialogue: 0,0:15:41.29,0:15:43.13,Default,,0000,0000,0000,,To the power.
Dialogue: 0,0:15:44.13,0:15:47.67,Default,,0000,0000,0000,,Of 0.
Dialogue: 0,0:15:48.84,0:15:50.10,Default,,0000,0000,0000,,Which is actually one.
Dialogue: 0,0:15:50.85,0:15:56.32,Default,,0000,0000,0000,,Which are very different meaning\Nto an angle. So you need to know
Dialogue: 0,0:15:56.32,0:16:00.95,Default,,0000,0000,0000,,the context to be able to decide\Nwhich one it means.
Dialogue: 0,0:16:00.96,0:16:05.62,Default,,0000,0000,0000,,Staying without superscript,\Nwe could have 32 degrees
Dialogue: 0,0:16:05.62,0:16:12.62,Default,,0000,0000,0000,,again, but this time with a\Ncapital C after it, and that
Dialogue: 0,0:16:12.62,0:16:17.28,Default,,0000,0000,0000,,would mean a temperature of\N32 degrees Celsius.
Dialogue: 0,0:16:19.58,0:16:22.54,Default,,0000,0000,0000,,Let's have a look at a couple of
Dialogue: 0,0:16:22.54,0:16:26.02,Default,,0000,0000,0000,,numbers now. It could be 6,
Dialogue: 0,0:16:26.02,0:16:28.54,Default,,0000,0000,0000,,three. Or it could be 63.
Dialogue: 0,0:16:29.30,0:16:30.78,Default,,0000,0000,0000,,Let's put a little bit more
Dialogue: 0,0:16:30.78,0:16:33.12,Default,,0000,0000,0000,,context there. If I put a comma
Dialogue: 0,0:16:33.12,0:16:38.88,Default,,0000,0000,0000,,between them. Then I know it's\Nnot 63, but I'm still not sure
Dialogue: 0,0:16:38.88,0:16:44.82,Default,,0000,0000,0000,,what the meaning is. It could be\Na number of things, but if I
Dialogue: 0,0:16:44.82,0:16:49.92,Default,,0000,0000,0000,,then put brackets around it, I\Nknow straight away that it's a
Dialogue: 0,0:16:49.92,0:16:51.20,Default,,0000,0000,0000,,pair of coordinates.
Dialogue: 0,0:16:51.27,0:16:58.79,Default,,0000,0000,0000,,And what it represents is\Nthe position 6, three on
Dialogue: 0,0:16:58.79,0:17:01.05,Default,,0000,0000,0000,,my coordinate axis.
Dialogue: 0,0:17:01.81,0:17:09.67,Default,,0000,0000,0000,,So I would go six\Nin the X Direction, 3
Dialogue: 0,0:17:09.67,0:17:17.53,Default,,0000,0000,0000,,in the Y direction and\Nthat is the position that
Dialogue: 0,0:17:17.53,0:17:20.67,Default,,0000,0000,0000,,that coordinate is representing.
Dialogue: 0,0:17:22.38,0:17:24.42,Default,,0000,0000,0000,,Now brackets may be used in a
Dialogue: 0,0:17:24.42,0:17:31.73,Default,,0000,0000,0000,,different way. If for example,\NI saw a pee and
Dialogue: 0,0:17:31.73,0:17:34.69,Default,,0000,0000,0000,,brackets H equals 1/2.
Dialogue: 0,0:17:35.45,0:17:39.86,Default,,0000,0000,0000,,I know that's actually nothing\Nto do with coordinates at all,
Dialogue: 0,0:17:39.86,0:17:42.67,Default,,0000,0000,0000,,and that is most likely to be
Dialogue: 0,0:17:42.67,0:17:49.29,Default,,0000,0000,0000,,probability. And that is\Nsaying the probability of
Dialogue: 0,0:17:49.29,0:17:51.88,Default,,0000,0000,0000,,event H happening.
Dialogue: 0,0:17:52.64,0:17:54.08,Default,,0000,0000,0000,,Is equal to 1/2.
Dialogue: 0,0:17:54.86,0:17:56.90,Default,,0000,0000,0000,,I don't know what that event is,
Dialogue: 0,0:17:56.90,0:18:00.30,Default,,0000,0000,0000,,I could. Surmise that it\Ncould be the probability,
Dialogue: 0,0:18:00.30,0:18:04.20,Default,,0000,0000,0000,,perhaps of scoring ahead when\NI toss a coin is equal to
Dialogue: 0,0:18:04.20,0:18:07.44,Default,,0000,0000,0000,,half, but I don't know I'd\Nneed more information, but
Dialogue: 0,0:18:07.44,0:18:10.04,Default,,0000,0000,0000,,certainly that it's something\Nto do with probability.
Dialogue: 0,0:18:11.63,0:18:14.100,Default,,0000,0000,0000,,Another symbol we use.
Dialogue: 0,0:18:15.00,0:18:17.74,Default,,0000,0000,0000,,The percentage symbol.
Dialogue: 0,0:18:18.32,0:18:25.18,Default,,0000,0000,0000,,This is familiar to us because\Nhere we've got our divide sign.
Dialogue: 0,0:18:25.76,0:18:28.98,Default,,0000,0000,0000,,And this means out
Dialogue: 0,0:18:28.98,0:18:36.05,Default,,0000,0000,0000,,of 100. So if we\Nhave for example 90%, it means
Dialogue: 0,0:18:36.05,0:18:38.22,Default,,0000,0000,0000,,90 out of 100.
Dialogue: 0,0:18:39.06,0:18:45.44,Default,,0000,0000,0000,,Let's look at\Na few more
Dialogue: 0,0:18:45.44,0:18:48.63,Default,,0000,0000,0000,,symbols, for example.
Dialogue: 0,0:18:49.14,0:18:51.96,Default,,0000,0000,0000,,R square root sign.
Dialogue: 0,0:18:53.72,0:18:59.77,Default,,0000,0000,0000,,An example here might be the\Nsquare root of 16.
Dialogue: 0,0:19:00.59,0:19:05.84,Default,,0000,0000,0000,,And it's the number that when we\Nmultiply it by itself gives us
Dialogue: 0,0:19:05.84,0:19:08.67,Default,,0000,0000,0000,,16. So the answer could be full.
Dialogue: 0,0:19:09.17,0:19:14.06,Default,,0000,0000,0000,,Or it could be minus four,\Nbecause minus four times minus
Dialogue: 0,0:19:14.06,0:19:15.84,Default,,0000,0000,0000,,four gives us 16.
Dialogue: 0,0:19:16.61,0:19:20.65,Default,,0000,0000,0000,,Now, often in printed material,\Nyou might just see the square
Dialogue: 0,0:19:20.65,0:19:24.68,Default,,0000,0000,0000,,root is just the tick without\Nthe line across the top.
Dialogue: 0,0:19:25.55,0:19:27.27,Default,,0000,0000,0000,,If you're writing it.
Dialogue: 0,0:19:27.81,0:19:32.13,Default,,0000,0000,0000,,It's clearer if you put the line\Nacross the top to include, so
Dialogue: 0,0:19:32.13,0:19:36.11,Default,,0000,0000,0000,,it's clear what you're including\Nin that square root sign. But be
Dialogue: 0,0:19:36.11,0:19:38.10,Default,,0000,0000,0000,,aware that you might just see
Dialogue: 0,0:19:38.10,0:19:44.32,Default,,0000,0000,0000,,the tick sign. Another symbol\Nthat's used as an X with a bar
Dialogue: 0,0:19:44.32,0:19:47.36,Default,,0000,0000,0000,,across the top and it said X
Dialogue: 0,0:19:47.36,0:19:51.26,Default,,0000,0000,0000,,Bar. And it means
Dialogue: 0,0:19:51.26,0:19:56.56,Default,,0000,0000,0000,,the mean. So it's the mean\Nof a set of numbers. Instead
Dialogue: 0,0:19:56.56,0:19:59.68,Default,,0000,0000,0000,,of writing the word mean, we\Nwrite X Bar.
Dialogue: 0,0:20:00.97,0:20:07.50,Default,,0000,0000,0000,,Another symbol, let's say we\Nhave one point 3.
Dialogue: 0,0:20:08.17,0:20:10.10,Default,,0000,0000,0000,,And we see a dot over the three.
Dialogue: 0,0:20:10.73,0:20:13.02,Default,,0000,0000,0000,,And this is our recurring
Dialogue: 0,0:20:13.02,0:20:18.83,Default,,0000,0000,0000,,decimal sign. And what that\Nmeans is we've got 1.3 and
Dialogue: 0,0:20:18.83,0:20:24.21,Default,,0000,0000,0000,,three 333 and it goes on\Nforever and ever reccuring, so
Dialogue: 0,0:20:24.21,0:20:29.59,Default,,0000,0000,0000,,the dot over the decimal place\Nmeans it goes on forever.
Dialogue: 0,0:20:31.00,0:20:36.16,Default,,0000,0000,0000,,We might have 1.317\Nfor example.
Dialogue: 0,0:20:37.37,0:20:39.39,Default,,0000,0000,0000,,And dots over the three on the
Dialogue: 0,0:20:39.39,0:20:42.53,Default,,0000,0000,0000,,7. Similarly, it means it goes
Dialogue: 0,0:20:42.53,0:20:48.43,Default,,0000,0000,0000,,on forever. But what it means\Nthis time slightly differently?
Dialogue: 0,0:20:48.43,0:20:53.57,Default,,0000,0000,0000,,Is this the 317 that's repeated\Nand goes on forever?
Dialogue: 0,0:20:53.58,0:20:59.92,Default,,0000,0000,0000,,In summary, mathematical\Nsymbols are precise
Dialogue: 0,0:20:59.92,0:21:03.08,Default,,0000,0000,0000,,form of shorthand.
Dialogue: 0,0:21:03.62,0:21:08.68,Default,,0000,0000,0000,,They have to have meaning for\Nyou. You need to understand them
Dialogue: 0,0:21:08.68,0:21:12.48,Default,,0000,0000,0000,,and to help with that\Nunderstanding. You have context.
Dialogue: 0,0:21:12.48,0:21:17.55,Default,,0000,0000,0000,,What else is with them and you\Nhave convention which is what
Dialogue: 0,0:21:17.55,0:21:20.50,Default,,0000,0000,0000,,mathematicians and scientists\Nhave decided. Certain symbols
Dialogue: 0,0:21:20.50,0:21:23.27,Default,,0000,0000,0000,,will represent. And that's\Nall you need to know.