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What's going on everybody!
Welcome to today's video on
geometry. My name is Jack Jenkins and
this is Academy of One.
Today we're going to be talking about the axiomatic
system. In this video, we are just
gonna be covering the axiomatic system.
Nothing else.
[Music] There are four parts to
the axiomatic system. The
undefined terms. The
definitions or defined terms.
The axioms or postulates.
And then the theorems.
Then using all the steps you'll be able to create a proof.
The undefined terms are the
terms that are self defined.
And we'll get into specifics in the next video,
So an example of an undefined term is
euclid. So euclid once said
a point is that which has no part.
We'll
what euclid. What is a part?
It doesn't make much sense. So instead of having
a definition to go with what a point is. Let's just
say a point is a point. Like
you know what a point is. If you don't know what a point is then
go back to pre algebra over there.
Cause you're not ready for geometry.
Defined terms are terms that have a
definition. Or they are composed
of undefined terms. For instance,
euclid said the ends of a line are
points. And that's pretty much the
definition of end points.
Axioms or postulates as there more commonly called
in geometry. Are statements about terms
that are true without evidence.
A prime example is the reflective
axiom. Which states that x =
x. For example, one
is equal to one and 2 = 2.
It's self explanatory.
An axiom is basically like...
no duh! But it's still
important in mathematics. Theorems
are the backbone of mathematics. They are
the statements we us by using terms
postulates and something called mathematical logic.
Which is a class I'm going to be doing in the future.
Theorems are usually stated as
if then hypotheses.
For instance, the
pythagorean theorem.
A squared + b^2 =
c^2. And
I'll get into the proof of that when I start doing my
class on proofs. We'll that's it for the
axiomatic system. Now I should
point out that in this particular course,
we're not gonna be writing a whole lotta
proofs. However, in the future of
geometry. When I plan on doing solid
state geometry or modern geometry. We're gonna
be definitely be using the axiomatic
system. And when I start my course on proofs.
Oh man, you guys are going to have a blast writing proofs.
I'm talking about five page long proofs here.
So as a recap,
there are four steps to the axiomatic proofs.
The undefined terms which
remember are terms that need no
explanation. The defined terms which have
definitions that are usually composed of undefined terms.
There are the axioms or
postulates. For now on I'm just gonna be calling
them postulates cause this is geometry.
So there are the postulates which are self
evident truths. And then there are the theorems
which are composed of terms and postulates
and logic that you can use to build
mathematical statements.
I hope you had fun with this video
and as we continue on our journey towards geometry
You are going to be understanding and seeing
postulates and proofs. And you
are just gonna be loving it. Again, we're not gonna be
writing very many proofs cause I'll save that
towards more interesting subjects later on in other
geometry courses but seeing
is believing. So
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have a great day everyone.
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