April 26 2024

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.

This is called the projectively extended real line.

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.

misc notes
## Exploring Spaces Comments

The number line doesn't have an end, you can keep dragging forever in either direction.

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.

Now you can move along the number circle by dragging clockwise and counterclockwise around the circle.

This is called the projectively extended real line.

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.

misc notes