Different kinds of 'number'

[christianp]

The number data type is a straightforward IEEE float at the moment. This is an easy solution that covers most kinds of number, but means authors need to understand all the edge cases or implement non-standard operations on top of floating point arithmetic.

It would be nice if we could add more number-like data types, so that the right behaviour happens automatically.

Examples of number-like types:

• [x] integers
• [x] fractions
• [ ] different fields (complex numbers, quaternions, Z_n (#109))
• [ ] percentages (displayed as (100*n)%; only exactly 0 should round to 0%; "percentage of" and "percentage change" have different meanings)
• [ ] ratios
• [ ] vectors and matrices of number-like data
• [x] measurements with units (#419)
• [x] arbitrary precision numbers, where the precision is specified in advance (#518)
• [x] scientific notation (mantissa and exponent handled separately, so precision is not lost when working with numbers on the same order of magnitude)

[christianp]

I learnt a good word recently: 'torsor'. The nLab says a torsor is "roughly speaking, a group that has forgotten its identity element". There's a slightly more understandable essay by John Baez.

Temperatures are examples of torsors: they can be compared, but there's no meaningful zero.