## Infinities & probabilities

Posted By on Feb 16, 2018

Emily takes a very intuitive approach to understanding the relative sizes of her lists (even, threeven, fiven, seven’n etc.) and the segments they create. However, we really should look a little deeper into the mathematics. Emily’s assertion that the lists of even and odd numbers are the same size is correct – because they are both infinite. Interestingly, when we combine the even and odd numbers we have all the...

## Emily’s Method

Posted By on Feb 11, 2018

When Emily makes the decision to exclude the even numbers from her threeven list she establishes her method to ensure that all her lists have unique elements. If we consider each list (even, threeven, fiven, seven’n etc.) to be a set then we can say that they are all disjoint.     She starts with a single, infinite set of positive integers with the prime numbers scattered throughout.     By applying her...

## Integer Sequences

Posted By on Feb 4, 2018

The sequences of integers that Emily finds in her exploration of numbers are well known to mathematicians. The On-Line Encyclopedia of Integer Sequences (OEIS) was started by Neil J. A. Sloane in 1964 and is a valuable open resource. Here are the lists of numbers that Emily created and their reference numbers: A000027 Everyday counting numbers (positive integers) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,...