Sets

[errant wolf]

If irrational numbers are broken down into algebraic and transcedental irrationals, then if algebraic irrationals are denumerable, is it true that the most general countable set that we can create is R - {transcedental irrationals} ?

[silk prism]

note that all transcendentals are irrational and that algebraic numbers are countable

but the question itself is meaningless

[errant wolf]

Maybe its meaningless but if we were asked nevertheless to construct the most inclusive set that is countable, it would be Q union {algebraic irrationals} right?

[silk prism]

there's no such thing as the most inclusive countable numerical set, you can always add just an element countably many times to get a countable set

[thorny solstice]

Flippo is still right, but there are also the computable numbers.

[silk prism]

recursive reals?

if construction here means algorithmical explicit one (with the real condition over the numerical set), then we need to take account of certain other definitions

[errant wolf]

okay I see where I'm wrong then

[errant wolf]

what are the computable numbers?

[thorny solstice]

Numbers that can be calculated to arbitrary precision in a finite number of steps

For example, e and pi

[errant wolf]

oke I see

anyways thanks for clearing my q up

.solved