MATHS BITE: The Cantor Set

And they call them “real” numbers!

mathsbyagirl

The Cantor Set is constructed in the following way:

Start with the interval [0,1]. Next, remove the open middle third interval, which gives you two line segments [0,1/3] and [2/3,1]. Again, remove the middle third for each remaining interval, which leaves you now with 4 intervals. Repeat this final step ad infinitum.

Cantor_set_binary_tree.svg.png

The points in [0,1] that do not eventually get removed in the procedure form the Cantor set.

How many points are there in the Cantor Set?

Consider the diagram below:

Screen Shot 2017-02-21 at 8.05.41 PM.png

An interval from each step has been coloured in red, and each red interval (apart from the top one) lies underneath another red interval. This nested sequence shrinks down to a point, which is contained in every one of the red intervals, and hence is a member of the Cantor set. In fact, each point in the Cantor set corresponds to a unique infinite sequence of nested intervals.

View original post 222 more words

Advertisements

Leave a comment

Filed under Uncategorized

My wordpress emails suddenly disappeared last night ??????

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s