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What's going on everybody! My name is Jack Jenkins
and this is Academy of One.
Today I'm gonna be talking about elementary number
theory and more number identities.
In this video, I'm gonna be refreshing
your memory. Then I'm gonna be talking
about rational and irrational numbers.
And lastly, I'm gonna be talking about
complex and imaginary numbers.
[Music]
[Music]. The natural
numbers are all positive numbers.
For instance, one, two three
centra. The whole numbers are
all the natural numbers plus zero.
The integers are all negative numbers, zero
and positive numbers. And the real numbers
are all numbers that are not imaginary
and that are not positive or negative
infinity. For more information on this, go ahead
and watch the video on number identities. It will
provide more information for you. [Music]
[Music]
[Music]. The rational
numbers are all numbers that can be written as
a ratio. Notice the first five
letters of that word. Rational, ratio.
That's how I remember it. For instance
is two a rational number.
Of course it is. You can write 2 as
2 over one. How about point 1.
yup. You can write that as one over
ten. How about let's say...
pie. No,
pie is not a rational number, because
a first of all, it's a constant, and b you
can't really write that as a fraction. The closest
you can get is twenty-two over seven. And that's not
really... it's not really pie
so you can't. As you can guess, an
irrational number is a number that can not be
written as a ratio. For instance,
let's take the square root of five
is that a rational number or an irrational
number, sorry. It is
it is! Because you can not write
that perfectly. The square root of five
equals 2.333333
33 and it countries on forever. You can not write that
as a ratio.
How about 64 or the square root of
sixty-four. It is not irrational.
Because the square root of 64 is eight and you can write
eight as eight over one. How about
pie. Of course it is. Because
it can't be written as a ratio as we talked about last slide
it is an irrational number.
And pie is equal to 3.1415
9 and it continues on forever.
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[Music]
A complex number, remember
is a number that has both real and
imaginary parts.
Go back and watch the imaginary video in the college
algebra series. So, let's
take two i is that imaginary. Yup.
How about seven times the square root
of negative one. We'll I equals
negative one so of course this is imaginary.
How about 789.
That has the real part but it doesn't have the
imaginary part. So it is not considered a
complex number. That's it for today's tutorial
on number Identities. Tune in
next time for when I'm gonna be talking about mathematical
elements and there inverse.
Alright, time for the plugs. You can go ahead
and visit academyofone.org for more information
on all our videos as we'll as to download the sides
and comment on the videos. You can go
ahead and email me at jack@academyofone.org.
jack@academyofone.org if you have any questions. And I'll answer
them either in the conclusion video at the end
or I'll answer them in the Q&A.
Just remember to email me
with the subject line of elementary number theory.
That way I can sort it easier.
Third is don't forget to subscribe to the youtube channel
and lastly, don't forget to
donate cause donating will help us produce better
quality videos. Alright, so have a great
day. [Music]
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