Computable Numbers

Almost all real numbers are non-computable.
Blows my mind.
Discuss.

Almost all
Talking about an infinite set.

HURR FUCKING DURR

>>2
HURR
DURR

Back to the imageboards, please

I suppose algorithms relying on "get a digit randomly" are disqualified then

>>2
Yes, meaning the set of computable numbers is countable.

>>4
If you were getting a random digit, then you wouldn't know which number you were computing, so yes, I don't think that qualifies.

>>2

Yes, almost all.

On a basic level, there are many different infinite cardinalities, so for example any countably infinite set is neglible in an uncountable one, and so it's complement can be considered to be 'almost all'

In a more precise way measure theory allows us to define sets of measure 0 and so a statement P(x) is said to hold 'almost always' if {x : not P(x)} has measure 0.

So for example, even an uncountable set can be neglible in an uncountable set with the 'obvious; (Lesbesgue) measure, consider for example the cantor set.

>>6
Stop talking out your ass, kid. Or at least spend a few more minutes on Wikipedia.

http://en.wikipedia.org/wiki/Almost
In set theory, when dealing with sets of infinite size, the term almost or nearly is used to mean all the elements except for finitely many.

Just admit that you (and OP if not the same person) have failed. Boo hoo. Get over it. Sage.

>>7
http://en.wikipedia.org/wiki/Almost_all

"...or "all but a countable set" (formally, a cocountable set); see almost.

When speaking about the reals, sometimes it means "all reals but a set of Lebesgue measure zero" (formally, almost everywhere). "

>>7
Kid? I'm doing a masters in maths. My post was informative and factually correct, something wikipedia is almost always not.

(Not OP)

>>9
Wikipedia physics and math articles are usually very good.

>>9
When it becomes a semantic battle - being able to tell OP is using correct semantics and not just "almost all" to just mean what it literally says - then you're grasping for straws.  I'd suggest trying a less obtuse argument.