L3 Real Numbers - Number System, Maths, Class 9 Video Lecture

hello friends this video on number
systems part 3 is brought to you by exam
fear calm
no more fear from exam so we talked
about national number whole number
integers
- number Arush it's not about real
numbers real numbers are the number
which you can plot in another line and
they're real number they exist for real
and that is denoted by ah okay so and
these real number
there's nothing but most rational number
and irrational number you combined these
two set of numbers to get real example
can be irrational mu 2 3 PI graphic MB
minus 1 0 1 by 2 3 by 2 stuff like that
all these numbers wish you can plot on
the number line a real number
ok definition of real number anything
which you can plot on the number line is
real number apart from the real number
is something called imaginary number in
real but they don't exist they are
imaginary that is denoted by I and there
is nothing but u dot minus 1 so we will
not talk about imaginary number in this
class maybe in the higher class you'll
understand imaginary number this is not
required as of norm understand then the
whole number system consists of real
numbers and imaginary numbers right
something nearby it will plus 3i 2 plus
isolate suppose this is an imaginary
part and this is the real part for now
not require real numbers the maximum we
are going to learn and real number is
nothing but you combine rational numbers
and international number what you get is
real number and real number is something
that you can plot on the number line
so every point every point on this
number line represents
this point it representing an opera from
this point it represents a reelin of 97
you can talk about this point it
represents a real number zero which
ourselves talk about something here so
it must be representing some real number
so in this case maybe four point five
nine two and that is a real number if
you want to not only hear it's diluted
and that is also a real number we'll
talk about that we'll see how we you
plot root 2 root 3 and stuff like that
on the number line but anything that you
can plot on a number line is really so
let me quickly brush in all these
concepts national number something which
you can count on fingers 1 2 3 4 right -
1 - 2 - 3 0 all these are not national
numbers 1 2 3 4 5 6 this is the national
number because you can count on fingers
whole number the only addition is 0 by
re become the int elastica since it has
a huge importance we are a new set of
numbers are together whole number it is
0 + natural number then we have integers
which has negative numbers as well and
then we have rational number which you
can write in the form of Eyk please note
- 1 - 2 - t are also rational number
because - 1 I can write as minus 1 by 1
minus 2 we can write as minus 2 ever and
these are all and then we have
irrational numbers which you can't write
in the bike you will create by all these
real irrational number irrational number
combined to form real numbers ok we'll
take some examples or real numbers are 2
and false
every whole number is a rational number
is it true or false so let's take let's
take a little number zero is zero the
national number answer is no that means
it is once don't take one like c1 I mean
take something which is exclusively a
whole number you say let's take a whole
number 3 and say is 3 all national
number answer is yes but do you have to
take all the numbers right
typically you take the numbers which has
patient with hole number that is soon
okay please don't be confused here
don't say that five is in a whole number
and pi is also natural number so you can
have a natural number which is the whole
number but not every whole number is a
natural number exception is so because
there is every year if you say the same
motion has some some whole number is a
national number answer is true right
because then you have one or two or
three as a whole number that's also a
national number so it should be very
careful about these words if it is some
this the whole segment is true if it is
every statement does the second is every
national number is a whole number so
natural number we know one two three
four this is the set of natural number
let's see one is a whole number yes
two is the whole number yes three four
all these numbers are whole number yes
that means every natural number is a
whole number it means each of every if
you say some some natural number is a
whole number in that case also it would
be because if you take four that is a
natural number hope you understand if
you see everything and all the numbers
in the rational number should be a whole
number if you say some even if one
national number is a whole number that
the condition is true okay a good
example to explain the difference
between every in some is for example if
I say every student watch exam here
videos watch exam here videos and I
think it is wrong State but not every
student washes I have here studios that
is a false statement but if I say some
students watch exactly your videos then
that is a true statement because yeah in
fact you are a student and you must
either watching exactly stupid example
your videos so this words actually are
very powerful words so please pay
attention to these words
okay the next example is every integer
is
number so let's see the integer set
integer set is minus 1 minus 2 minus 3
like that also zero plus 1 plus 2 okay
and if you see all of these are actually
a rational number and rational number
has extra numbers like -2 minus 1 by 2 2
by 7 3 by 2 so anyone anything which is
an integer has to be large number so
this statement is please pay attention
here but the flip side will not be true
you can see this this is the flip side
every rational number is an integer say
rational number example can be plus 1 by
2 minus 1 by 2 minus 1 plus 1 0 right
all these are examples of rational
number now if you see plus 1 by 2 is not
an integer minus 1 by 2 is not an
integer but these are integers so this
statement is false but if you change
every to sum and if you say some
rational numbers are integers then the
answer is true because minus 1 is a
rational number and it is an integer
okay every rational number is a whole
number so let's the example of rational
number rational number can be 1 by 2
minus 1 by 2 whole number is 0 1 2 like
that so if you see 1 by 2 actually is a
rational number but it is not a whole
number correct so this statement is also
false so the question is is every
integer a whole number please note the
word every and you see the integers
integers a minus 1 minus 2 minus 3 0 1 2
3 stuff like that
are these 4 numbers if you see - not - 2
- 3 they are not this will be possible
ok so if you make it some in two years
is a whole number then it is true
because these are whole numbers 0 1 2 &
3 but for this question answer way was
so if my question is some integers
our whole number then the answer will be
yes true
the next example is every irrational
number is the real number true or false
so let's see the irrational number set
to 3 PI these are a rational number and
if you see all of these irrational
number are real number actually we have
seen that real number is nothing but
rational number and here rational number
combined so it is a true statement
the next is other way round every real
number is irrational number so if you
see the real number real number also
includes number like 1 2 3 4 5 right 0
all these numbers are not irrational
right these are rational numbers so this
is false so the question say is every
point on the number line is root M where
m is a natural number we have to see
this
so let's see this point what is this
point is fine is 0 and 0 will be equal
to root 0 but 0 is not natural right you
talk about minus 4 minus 4 is root of
nothing you cannot write minus 4 a suit
of anything right you you can write plus
4 as root of 16 but minus 4 you can't
write root of any number a number is not
there so that I can say that every point
on the number line is not root M number
minus 4 and 0 because it's call saying
that M has to be national so this is the
false statement please pay attention
here the questions say that every point
on the number line is don't M
is an acronym and we have seen that
minus four is a point which cannot be
represented as root M where m is a
national level even zero can't be
represented as root M whereas a national
number is zero or rational number see
the rational number is something which
you can write in the Hokie by Q Q is not
equal to zero and P and Q are integers
zero I can write as zero by one where 0
and 1 both are integers and one is not
equal to zero
nd weighted the zero is a rational
number
okay let's take some examples you will
find six rational number between 3 and 4
this is 3 this is 4 so what I told since
6 such numbers are required I'll
multiply by 10 by 10 I can multiply by
100 by hand as well but just to simplify
the calculation this is 30 by 10 this is
40 by 10 so let's find some numbers
between 35 to 40 by 10 31 by 10:30 to by
1033 by 10:30 10:35 by 10 these are 6
rational numbers between 3 and in fact
as we discussed they are infinite number
of rational numbers between any two
rational numbers
yeah fine 5 watch another 3 by 5 8 4 or
5 so 3 by 5 and X inside to find only 5
rational numbers I'll multiply by 10 by
10 the same so this becomes 30 by 50 and
this is let's find rational between them
but the one my 52 by the t-33 by 50 34
by 55 by 50 and the list continues but
we want only five Silla stopped at 5
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