Mapping an Interval to Another

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

There is a one-to-one and onto mapping between any two intervals. The intervals can be of different sizes, infinite, open, closed, or half-open. By composing the mappings shown here, sometimes with slight modifications, you can find a mapping between any two types. Therefore any two intervals have the same number of points. In fancier language, any two intervals are equipotent and have the same cardinality as that of the real numbers.

[more]

The last case (half-open to open), is not a continuous map and has a countable infinity of jumps near the origin.

[less]

Contributed by: George Beck (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

detailSectionParagraph


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send