Hello, this is MutatedRedstone from PowerCraft
once again and today, we'll divide numbers
by 0 in Minecraft.
This video is a thank-you to you guys who
have supported me for 7.5 years.
We've amassed over 1200 subscribers and it
couldn't be possible without your support.
Anyway, let's get right into the video.
So, this is the real number line that we're
all familiar with:
Negative numbers to the left, 0 in the middle,
and positive numbers to the right.
With this way of constructing real numbers,
it's impossible to divide by 0, but mathematics
is an abstract field of study whose rules
can easily be bent.
So, behold, the projectively extended real
number line.
This set of real numbers is denoted by R-hat,
and it also includes ∞.
On this circle, you can represent every real
number but also ∞.
To show this, we can illustrate how numbers
can be projected into the real number line.
We need to draw a line from the point of ∞ to
the position of the number on the circle and
extend it to the real number line between
1 and -1.
So, let’s just do that.
As you can see, 2’s position on the line
corresponds to its position on the circle,
and the same is true for -½.
Since we can't draw a line from ∞ to itself,
∞ can't be represented on this line.
That's why we need to use this circle to define
division by 0, we need ∞.
Here are the operations that we can do using
this set, take a look.
Any number divided by 0 is ∞, and ∞ divided
by any number is ∞.
One important property is that ∞ equals
-∞, which means that vertical asymptotes
of the functions only approach this number (on
the technical side).
If you have any questions, ask in the comments.
No matter how hard it seems like we're pushing
the limits of abstract mathematics, this projectively
extended real number line has some limitations.
So, take a look.
These operations aren’t defined in the set
that we’re talking about.
In reality, there's also a way to define these,
which is way more complicated than the one
we’re doing right now.
However, depending on your feedback, I may
do a follow-up video explaining the brilliant
structures where these operations are also
defined.
If you want it, don't forget to like and share
the video, and become part of the PowerCraft
family by subscribing.
See you in the following videos. Bye!
