Mathematics
Heads, Tails And Beans |S|=4
So far, we’ve looked at sets and how they contain information that we wish to count in some way. How the power set \(\wp(S)\) can count all of the possible sub-sets of a given set [more…]
Mathematics
Mathematics
Heads, Tails And Beans |S|=3
Subsets Let’s suppose that set \(S\) contains a full deck of playing cards. Therefore, \(|S|=52\). We can split the cards into four suits: \(♠,♣,♥,♦\). Let’s make a set \(T\) that contains only the clubs suit [more…]
Mathematics
Heads, Tails And Beans |S|=2
Before we can start to solve some counting problems we need to know a little of combinatorics’ notation. Luckily, a few simple rules should get us started. Don’t worry if it doesn’t make sense, that [more…]
Mathematics
Heads, Tails And Beans |S|=1
Mathematics is not everyone’s cup of tea – fair enough. The Monday morning ‘double maffs’ articles by our resident mathematician, OldTrout, can present some GP’ers with a feeling of bewilderment. Myself included. I’m no mathematician. [more…]
Hobbies
The Infinity of the Primes
Euclid’s Elements, Book IX, Proposition 20. Theorem : Prime numbers are more than any assigned multitude of prime numbers. That is, there are infinitely many primes. Proof : Suppose that there are primes : [more…]
Arts
BBC Climate Change Bias
Following my previous piece on the Business of Climate Change I thought you might be interested to know a little more about the BBCs Climate Change Bias, just how it came about and how BBC [more…]
Mathematics
Where Astrophysics meets Climate Science
– Astrophysicists have succeeded in decoding Solar activity and the results show that climate scientists have some questions to answer. There is an interesting collision about to take place between astrophysics and climate science. This [more…]
Hobbies
Distinct and Odd Partitions
Euler’s Partition Theorem: The number of distinct partitions of an integer, , is equal to the number of odd partitions of that integer : , for all . Euler gave us a proof which is [more…]
Computing
Computing Partitions
Euler gave us the following recursion formula for via his Pentagonal Number Theorem : Note the generalised pentagonal numbers in the above. Define if and let . This is the formula that [more…]