Archives for Number Theory
Uncountability of (0,1): Cantor’s Diagonal Argument
The Reals in \((0,1)\) Are Not Countably Infinite See also - Cardinality of the Rationals - Positive and Negative included Claim The interval \((0,1)\subset \mathbb{R}\) is uncountable. Equivalently, there is…
Cardinality of the Rationals (Including Negative Rationals)
Also read 'Cardinality of the Reals' Do Negative Rationals Change the Cardinality? Short answer: No. Adding negative rationals keeps the set countably infinite, the same cardinality as the integers \(\mathbb{Z}\).…
The Monster Group in mathematics
The Monster Group, often referred to as the "Monster" or M\mathbb{M}M, is the largest sporadic simple group in mathematics. It plays a significant role in the field of group theory,…
Perfect Numbers – and a best case algorithm
Brute Force Algorithm - O (N) The brute force approach will loop through all the way from 1 to N - looking for divisors and add them to a running…