rationals

Edit: > You can describe it with one or two rationals (Edit: two or four for 2D).

You can describe it with one or two rationals (Edit: two or four for 2D).

But it does imply that the set of limit points of all countably infinite series of rationals is uncountable.

You could even label each pixel by its bordering line, and then you're literally counting rationals.

Here's another way of looking at it: the number of pixels obtained by division by countably many lines is equal to the number of subsets of the rationals--which is uncountable.

Assuming that they must be the same is the equivalent of assuming that the cardinality of the reals is the same as the cardinality of the rationals, which is obviously false.

In constructivism, once you have a Cauchy sequence of rationals, that represents a real.

But bigdecimals (or even arbitrary precision rationals) may be preferred in certain financial applications.

Nitpick, under standard definitions, 2 is a unit, over the field of rationals (or reals, or many other systems).

Anyway I accept that with normal semantics you can't define non-point non-overlapping ranges between dense rationals.

Seems odd, considering the figure I've heard quotes Rationals as 10% of the US population.

Second, outputting an irrational number as a measurement does not imply that it's able to output any member of the complement of the rationals in the reals.

Don't you find it at least interesting that HN readers are 7 times over represented in the "NT" or "Rationals" class?

Considering the one-dimensional case for a second: if you define a pixel with two "rationals" (I think you mean two numbers of the form k/2^n here, you're describing (I presume) its left and right boundary, creating an interval (a, b) where a < b.

In the mentioned context of the reals, or even just the rationals, we could instead note that 6 (or anything, really) could continue being divided indefinitely, thus having no particular "prime factorization" in the sense of a factorization which cannot be further refined.

The argument to which I responded, and which I extended absurdly, does imply that every real number is a valid output of a chance setup, and further assumes that each real number, including "any member of the complement of the rationals in the reals", is an equally likely outcome of that setup.

If you really think the test is bullshit, then why am I, and the vast majority of the respondents on the previous poll (linked above/below) NTs, also know as Rationals?