What question did this study set out to answer?

The aim is to determine if the functions ln, arctan, and cos can be expressed using more basic mathematical operations.

March 26, 2026Open Access

URB #507: The Minimal Basis — i, +, −, ×, ÷, lim Generates All of Mathematics

Key Points

The aim is to determine if the functions ln, arctan, and cos can be expressed using more basic mathematical operations.
Exploration of the derivation processes for ln, arctan, and cos.
Analysis of mathematical operations such as {+, −, ×, ÷}.
Examination of the implications of reduction on primary constants.
Identified potential connections between primitive operations and the specified functions.
Found that certain functions might not need additional complexity to be derived.

Abstract

URB #506 established that all 8 PRIMARY CONSTANTS are derivable from i using the operations +, −, ×, ÷, ^ (1/n), ln, arctan, cos, lim. This paper asks: **can ln, arctan, and cos themselves be reduced to more primitive operations? **

URB #507: The Minimal Basis — i, +, −, ×, ÷, lim Generates All of Mathematics

Key Points

Abstract

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