If a number has an infinite decimal.expansion, it is irrational, and if there is a finite programme that spits out the digits indefinitely, then it’s computable. There is a countable infinity of programmes, but an uncountable infinity of irrational.numbers, so most irrational numbers are uncomputable.
I definitely associate rationals with “the numbers my computer has problems printing or representing internally
You seem to be thinking in terms of fixed length representations. Although widely used , they are not essential to computation, and don’t feature in theoretical
computer science.
(Sorry my Bad. I meant irrational in the previous comment) Yeah, I get that you can do it differently. I meant that you can’t just naively store all the digits. Did minimal googeling and and found the Wikipedia article on computable numbers and it lists all kinds of representations that I would never have thought of.
If a number has an infinite decimal.expansion, it is irrational, and if there is a finite programme that spits out the digits indefinitely, then it’s computable. There is a countable infinity of programmes, but an uncountable infinity of irrational.numbers, so most irrational numbers are uncomputable.
You seem to be thinking in terms of fixed length representations. Although widely used , they are not essential to computation, and don’t feature in theoretical computer science.
(Sorry my Bad. I meant irrational in the previous comment) Yeah, I get that you can do it differently. I meant that you can’t just naively store all the digits. Did minimal googeling and and found the Wikipedia article on computable numbers and it lists all kinds of representations that I would never have thought of.