4 ms·
Only for rational numbers. Decimal -> fraction is a surjection. Irractional numbers, notionally representable as decimals, are uncountably infinite, and do not
by tomrod 4y ago
Only for rational numbers. Decimal -> fraction is a surjection. Irractional numbers, notionally representable as decimals, are uncountably infinite, and do not map 1:1 to fractions.
- mbg721 4y agoIt is literally a ratio of integers, therefore rational.
- tomrod 4y agoCorrect, rational numbers are those numbers that can be represented as a ratio of integers (excluding zero as denominator). Our points agree.
- mitthrowaway2 4y agoIt is rational: 391/1250
- tomrod 4y agoThis particular value is, certainly.
- mitthrowaway2 4y ago(Note: this was a mistyping of 381/1250)
- throwthere 4y agoI think you’re technically equating non terminating to irrational but the looser point seems fair to me— it’s hard to codify precise decimals.
- tomrod 4y agoClose. Many non-terminating can be mapped to fractions (e.g. 0.88888... = 8/9), which is equivalent to rational, but non-terminating and non-repeating are irrational (e.g. π or e).
- throwthere 4y agoI guess I’m just making the point all nonterninating are hard to codify in non mathematical fonts formatting etc. For instance using that 0.88888 example, that decimal very much does not precisely equal 8/9. you’d either have to keep writing 8s into infinity or hope everybody who copies/Padres your writing has a way to preserve the indicator of repeating digits.