## www.mathcentre.ac.uk/.../mathematical%20language.mp4

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Mathematics has its own
language, most of which which
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were very familiar with. For
example, the digits 012.
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345678 and nine are part
of our everyday lives, and
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whether we refer to this
digit as zero.
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Nothing.
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Note
Oh oh, as in the
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telephone code 0191 we
understand its meaning.
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There are many symbols in
mathematics and most of them are
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used as a precise form of
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shorthand. We need to be
confident using the symbols and
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to gain that confidence, we need
to understand their meaning.
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To understand that meaning,
we've got two things to help us,
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there's context. What else is
with the symbol? What's with it?
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And this convention and
convention is where
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Mathematicians and
scientists have decided that
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particular symbols will
represent particular things.
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Let's have a look at some
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symbols. That sign words
associated with it
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a plus. That
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Increase.
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And positive. As
it stands, it has some form of
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meaning, but we really need it
in a context. For example, 2 + 3
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or two ad three. We know the
context, we add the two numbers
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and we get 5.
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Let's have a look at another
context. Now, if you've gone
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abroad, say to Europe, and you'd
gone to a conference, you might
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that people could contact you.
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number, so chances are it will
be written as plus 44, and let's
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have a phone number 1911234567.
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And in this context, that plus
means that the person dials the
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necessary code for an
international line from their
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country, then 441911234567.
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So it still means In addition
to, but not in the same way as
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that plus sign were not actually
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Let's have a look
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now. At this
sign.
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Well, it's associated with this
one and minus.
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Subtract. Take
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away.
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Negative.
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And decrease.
And again, we need a context.
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Let's six takeaway four or six.
Subtract 4 and we all know the
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In a different context, if we
have minus 5 degrees C for
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example. That means a
temperature of five
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degrees below 0.
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Words associated with
this symbol multiply.
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Lots of. Times Now
this one is really just a
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Let's have a look at the
context. For example, six at 6,
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at 6, at 6 at 6.
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What we've actually got a
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123456 is. And in short
hand we want to write 5 sixes.
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On the symbol that's used is the
multiply sign, so we've got five
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lots of 6 or 5 * 6.
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Now this shorthand becomes even
shorter when we use some letters
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So for example, instead of six,
let's say we were adding AA
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again, will have 5 days.
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But because we've used the
letter, if we use the multiply.
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It could be confused
with the letter X.
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So we don't write it in.
Basically we miss it out and we
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just write 5, eh? So the
shorthand becomes shorter, so
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when letters are involved, the
multiply sign is missed out is
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the only symbol that we miss
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out. Let's look
at division.
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Now this symbol can actually be
written in three different ways.
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We could have 10 / 5.
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10 / 5 as it's written in a
fraction or 10 with a slash
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and five now this ones come
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printing and typing and using
a computer. When these
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available on the keyboard.
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So how many times does 5 go
into 10 or 10 / 5?
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Another very common symbol that
we use all the time without
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thinking is the equals sign.
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Again, it doesn't mean anything
on its own. We need it in some
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form of context. So if we have
the sum 1 + 2 equals 3.
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What we're saying is whatever we
have on this side is exactly
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equal to. Whatever we have on
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this side. Or it's the same as?
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Variations on the
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equals sign. Of the
not equal sign, a line through
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the equals which is not equal
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to. For example, X is not
equal to two.
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So we know that X does not take
that value of two.
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Two WAVY lines without
equals means approximately
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equal to.
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So it may not be
exact, but it's approximately
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equal to that value.
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Are greater than
or equal sign?
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An example here
might be X
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is greater than
or equal to
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two. That means X could take the
value of two, but it could be
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any number larger than two.
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And are less
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than. Or equal
2.
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I'm here for example. Why would
be less than or equal to 7?
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Why could equals 7? But it could
be any number less than 7.
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And an easy way of remembering
which is the greater and the
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less than part is the greater
is the wider part of the
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symbol, whatever's on the
wider part of the symbol,
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whatever's on that side is the
greater than the one where the
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point is on the other side.
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Other forms
of mathematical
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symbols are
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variables. I'm
basing used where things
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take different values.
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For example, imagine your
journey to work in your car.
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And imagine the speed that
you're traveling at as you go
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speed will change, so we
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might refer to the speed with
a letter. Let's say the
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letter V, because throughout
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numerical value is changing.
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We usually use letters for
variables, letters of the
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alphabet. You can call them
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anything. But we try to use
letters of the alphabet and we
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try to have those letters giving
us some indication of what our
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For example, we might use
deep for distance.
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And T for time.
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By convention, we use you to
be initial speed.
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And V to
be our final
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speed. But of course, we
might also refer to volume.
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And This is why context is
important and we look to see
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what a variable is with as to
what it might mean. So, for
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example, if we were to CV is D
divided by T.
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And we're told that Diaz
distance and T is time. Then we
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know that that V is speed.
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Whereas if we saw V
with Four Thirds Paillard cubed.
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Where are is the radius of a
sphere. We know that that V is
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also the volume of a sphere.
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Now going back to our example
again of our journey to work, we
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might want to record the time it
took us to go to work, and we
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might want to do that over a
number of days.
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The most sensible variable to
use would be a T for our time.
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But of course, if we want to
record it for each day, how do
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we distinguish between the TS?
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Well, in this case we
use a subscript.
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So for day
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one. We might
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use T1. The
next day to
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223-2425. Or we might want
to be a little bit clearer and
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actually put perhaps TM for the
time on Monday TT for Tuesday
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TW. For Wednesday we would have
to do TH for Thursday so it
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doesn't get confused with
Tuesday and TF for Friday, so we
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can use these subscripts small
numbers or letters at the bottom
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right of the variable to
distinguish between them.
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Now, by convention,
mathematicians have decided that
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we're going to use some
letters of the Greek alphabet
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for some of our mathematical
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symbols. For example,
we have pie.
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Empires being chosen to equal
the number 3.14159 and it
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goes on and on forever,
never repeats itself.
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And so that we can precisely say
what we mean, rather than having
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to round the value.
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We use the letter Pi knowing
that it's that number.
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From the Greek alphabet we also
use some other letters such as
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Alpha. 's
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pizza. And
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feature. Now, these
are often used as variables to
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represent angles. So you might
see an angle marked in that way,
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and the Greek letter Theta.
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Another one that is commonly
used is a capital Sigma.
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Now you should be familiar with
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program on a computer, because
you'll find it somewhere on the
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toolbar because it means the sum
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of. And it's a shorthand for
adding up a column or a row of
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numbers on a spreadsheet. So it
means the sum of.
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The positioning of where we put
letters or figures without
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symbols. Has gives meaning to
it, just like our subscripts we
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can have superscripts now
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at the bottom right, go at the
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top right. So for example, for
the little two at the top right
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hand side, that's a superscript.
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And again, it's a shorthand as
most of our symbols are and that
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means 4 squared.
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4 *
4.
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If we have 4 cubed.
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We've got three of them,
4 * 4 * 4.
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Alright, a number that means to
the power of.
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So we've raised 4 to the power
of three 4 * 4 * 4.
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32
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With the 0 as a superscript now
this is actually got two
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meanings. And we need the
context to be able to know which
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meaning it is. It could
be 32 degrees.
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And that would mean an angle.
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Of 32 degrees.
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But it could mean 32.
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To the power.
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Of 0.
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Which is actually one.
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Which are very different meaning
to an angle. So you need to know
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the context to be able to decide
which one it means.
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Staying without superscript,
we could have 32 degrees
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again, but this time with a
capital C after it, and that
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would mean a temperature of
32 degrees Celsius.
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Let's have a look at a couple of
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numbers now. It could be 6,
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three. Or it could be 63.
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Let's put a little bit more
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context there. If I put a comma
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between them. Then I know it's
not 63, but I'm still not sure
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what the meaning is. It could be
a number of things, but if I
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then put brackets around it, I
know straight away that it's a
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pair of coordinates.
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And what it represents is
the position 6, three on
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my coordinate axis.
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So I would go six
in the X Direction, 3
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in the Y direction and
that is the position that
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that coordinate is representing.
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Now brackets may be used in a
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different way. If for example,
I saw a pee and
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brackets H equals 1/2.
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I know that's actually nothing
to do with coordinates at all,
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and that is most likely to be
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probability. And that is
saying the probability of
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event H happening.
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Is equal to 1/2.
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I don't know what that event is,
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I could. Surmise that it
could be the probability,
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I toss a coin is equal to
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half, but I don't know I'd
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certainly that it's something
to do with probability.
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Another symbol we use.
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The percentage symbol.
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This is familiar to us because
here we've got our divide sign.
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And this means out
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of 100. So if we
have for example 90%, it means
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90 out of 100.
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Let's look at
a few more
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symbols, for example.
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R square root sign.
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An example here might be the
square root of 16.
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And it's the number that when we
multiply it by itself gives us
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16. So the answer could be full.
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Or it could be minus four,
because minus four times minus
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four gives us 16.
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Now, often in printed material,
you might just see the square
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root is just the tick without
the line across the top.
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If you're writing it.
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It's clearer if you put the line
across the top to include, so
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it's clear what you're including
in that square root sign. But be
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aware that you might just see
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the tick sign. Another symbol
that's used as an X with a bar
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across the top and it said X
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Bar. And it means
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the mean. So it's the mean
of a set of numbers. Instead
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of writing the word mean, we
write X Bar.
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Another symbol, let's say we
have one point 3.
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And we see a dot over the three.
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And this is our recurring
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decimal sign. And what that
means is we've got 1.3 and
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three 333 and it goes on
forever and ever reccuring, so
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the dot over the decimal place
means it goes on forever.
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We might have 1.317
for example.
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And dots over the three on the
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7. Similarly, it means it goes
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on forever. But what it means
this time slightly differently?
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Is this the 317 that's repeated
and goes on forever?
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In summary, mathematical
symbols are precise
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form of shorthand.
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They have to have meaning for
you. You need to understand them
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and to help with that
understanding. You have context.
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What else is with them and you
have convention which is what
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mathematicians and scientists
have decided. Certain symbols
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will represent. And that's
all you need to know.
Title:
www.mathcentre.ac.uk/.../mathematical%20language.mp4
Video Language:
English
Duration:
21:24
 mathcentre edited English subtitles for www.mathcentre.ac.uk/.../mathematical%20language.mp4 Emma Cliffe edited English subtitles for www.mathcentre.ac.uk/.../mathematical%20language.mp4 EHCliffe edited English subtitles for www.mathcentre.ac.uk/.../mathematical%20language.mp4 EHCliffe edited English subtitles for www.mathcentre.ac.uk/.../mathematical%20language.mp4 EHCliffe edited English subtitles for www.mathcentre.ac.uk/.../mathematical%20language.mp4 EHCliffe edited English subtitles for www.mathcentre.ac.uk/.../mathematical%20language.mp4 EHCliffe edited English subtitles for www.mathcentre.ac.uk/.../mathematical%20language.mp4 EHCliffe edited English subtitles for www.mathcentre.ac.uk/.../mathematical%20language.mp4