This is an end-of-year count of the number of 3-legged dogs in my life.
In a previous post I described how Suki entered our lives 2 years ago.
The story of Rolo is more complex, but essentially we looked after him for about a year, while his owner was temporarily unable to do so.
Rolo and Suki were different in breed, size, age, gender, speed, willingness to bark, and propensity to chew the post – but clearly found they had something in common…
It’s a shift of gear I know, but this is a good opportunity to introduce (mathematical) sequences. An item on radio 4’s More Or Less caught my imagination, relating to a specific (mathematical) series. And this reminded me of several other series worthy of comment; the upshot being that I first need to explain sequences.
A sequence is ‘an ordered set of mathematical objects’. For mathematical objects read numbers – or perhaps expressions that evaluate to numbers – so the 52 numbers above is a sequence. 1,2,3 is a sequence, and because order matters it is different to the sequence 2,1,3. These are finite sequences, the first has 52 terms, the other two have 3.
Mathematicians find more interest in those that go on for ever: infinite sequences. We could have an infinite sequence of 1s: 1,1,1,1,1,… or all the whole numbers: 1,2,3,4,5,… There are two key areas of interest: do the terms of the sequence eventually settle down to a fixed number (convergence), and what happens when you add up all the terms of a sequence (series).