In previous works, authors wrote equality expressions in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by single or double equality signs. These expressions are based on the idea of **crazy representations** of natural numbers. These equality expressions are based on basic operations along with **factorial, square-root, Fibonacci sequence** and **triangular numbers values**. These types of equalities, we called as **crazy running equality expressions**. This work is revised and enlarged version of author’s previous works, where the basic operations along with factorial, square-root are considered. It is not possible to write all the natural numbers in terms of **crazy running equality expressions**. Only the possible numbers are written. The work is up to 6 digits:

Link for download:

- Inder J. Taneja, Crazy Running Equality Expressions With Factorial and Square-Root,
**Zenodo**, December 06, 2021, pp. 1-464,**https://doi.org/10.5281/zenodo.5761752**

See few examples below:

**Previous work for donwload:**

- Inder J. Taneja, Running Expressions in Increasing and Decreasing Orders of Natural Numbers Separated by Equality Signs, RGMIA Research Report Collection,
**18**(2015), Article 27, pp.1-54,**http://rgmia.org/papers/v18/v18a27.pdf**. - Inder J. Taneja, Running Expressions with Equalities: Increasing and Decreasing Orders – I, RGMIA Research Report Collection,
**20**(2017), Art. 33, pp. 1-57,**http://rgmia.org/papers/v20/v20a33.pdf**. - Inder J. Taneja, Running Expressions with Equalities: Increasing and Decreasing Orders – II, RGMIA Research Report Collection,
**20**(2017), Art. 34, pp. 1-87,**http://rgmia.org/papers/v20/v20a34.pdf**.

**Recent work for download:**

- Inder J. Taneja, Crazy Running Equality Expressions With Factorial and Square-Root,
**Zenodo**, December 06, 2021, pp. 1-464,**https://doi.org/10.5281/zenodo.5761752**

**Results with Fibonacci Squence and Triangular numbers:**

- Inder J. Taneja, Fibonacci Sequence and Running Expressions with Equalities – I, RGMIA Research Report Collection,
**20**(2017), Art. 35, pp. 1-83,**http://rgmia.org/papers/v20/v20a35.pdf**. - Inder J. Taneja, Running Expressions with Triangular Numbers – I,
**Zenodo**, December 21, 2018, pp. 1-142,**http://doi.org/10.5281/zenodo.2483327**.