Try dragging the number line left and right to change the position of the
point
.
The number line doesn't have an end, you can keep dragging forever in either
direction.
Squeezing All Numbers Into a Single Paragraph
By making each number take up less space than the last, we can fit them all
into a box!
It's the same number line, but now its like you can see both sides going off
into the distance and out to infinity.
I added two points connected to either end labelled -∞ and +∞. When you add
these two points to the number line, the space is called the
extended real number line. You can still never reach these points by dragging left or right, but
nevertheless, they are attached to the line.
Taping -∞ and +∞ together
If you've read the other two posts in this series or read the title of this
one, you may have seen this coming... I've bent the number line into a
circle and
taped together -∞ and +∞!
Now you can move along the number circle by dragging clockwise and
counterclockwise around the circle.
If you want to see how to add, subtract, multiply, and divide in these two
spaces, check out the links! (You can even divide by 0 in the projectively
extended real line)
The infinite number line is similar to a finite line; lines can be bent or
taped into a circle whether they are finite or infinite.
I made
this post to try to illustrate that infinite spaces are not intangible or
impossible to play around with.