Just had what I consider to be an interesting discussion with Dan (MSE Researcher), who has a degree in Maths from Imperial College, London. We were discusssing the concept of infinity, based on a question my Uncle asked me when I was 11 (and you wonder why I am the way I am?)
He said, if there are an infinite number of numbers betwen 1 and 2 (ie. 1.01, 1.001, 1.0001 etc) and an infinite number of numbers between minus infinity and plus infinity, then are there more numbers between -infinity and +infinity than between 1 and 2?
Whilst logic says yes. Mathematics says no, they’re both the same answer. Then comes the difficult part, trying to work out how they can both be the same. Eventually we came up with a visualisation. If you have one circular path around the world, which you walk on for ever, you still walk the same length as you would on a spiralling path that goes many times around the world, looping much more.
If you’re still awake and want to discuss this, please reply here
