Idle thoughts and unanswerable questions on a Saturday morning:
The Number System seems to be continuous and infinite but every number seems to be discrete. But if any number is also infinitely divisible it must also be continuous. So are numbers simultaneously both discrete and continuous?
Or is a number just a label? Perhaps a number – if just a label and representing a singularity – is discrete and the divisibility of a number is actually undefined. It is number difference – not a number – which is infinitely divisible. So – for example – the number 10, as a label, is not divisible — it is the number difference between 10 and some reference number (10-0) which is. So is our Number System then a discrete thing and made up of an infinite and continuous quantity of number differences with each number difference being discrete? It would then be rational for there to be an infinity of discrete Number Systems.
So perhaps numbers don’t exist. Only number differences do and the numbers are their labels.
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