Silly thought by a non mathematician
I'm totally prepared for a mathematician to tell me that this is complete rubbish!
Having read about hyperreal and hyperinteger numbers I thought what if we had a number system base H where H is a hyperinteger.
Each column could potentially have a symbol representing 0 or any one of the counting numbers (yes I know that's an infinite number of symbols!). The first column could on its own represent any natural number itself. The the first colun to the left would represent multiples of H, then H^2, H^3 and so on. This is where it gets interesting.
Each column represents a different order of infinity. The units column represents multiples of any counting numbers, but not hyperintegers, The next column represents any counting number of multiples of H, but not H multiples of H and so on. This implies that there can never be any carry or borrow between columns with normal arithmetic operations solely acting on members of the column. This means that unlike normal bases each column represents something fundamentally different. Maybe it would make more sense to allow symbols for any integer, making it a balanced base!
As this is getting long I will continue in another post looking at the columns to the right past the "decimal" point, of course it's not decimal I'll call it the H-point.
#math #maths #mathematics #hyperreal #infinity #infinityAndBeyond #musings