Are real numbers really real?

Re:Are real numbers really real? by rocqua on Tuesday June 12, 2018 @02:37PM (#17296447)

That gives every terminating decimal or binary number. For example, you will never list 1/3, or pi or sqrt(2).

To see why you cannot generate every possible real number as a list, look up cantors diagonal argument.

[ Parent | on HN ]

Re:Are real numbers really real? by windows_tips on Tuesday June 12, 2018 @04:15PM (#17297553)

Are you sure 1/3 is a real number?

[ Parent | on HN ]

Re:Are real numbers really real? by filmor on Tuesday June 12, 2018 @04:44PM (#17297800)

Real numbers are defined as a particular extension of the rational numbers, which 1/3 is.

[ Parent | on HN ]

Re:Are real numbers really real? by rocqua on Wednesday June 13, 2018 @01:58PM (#17305510)

"Real numbers" here refers to a very specific construction of numbers. There is pretty good argument, which the actual post is about, that states this construction is actually rather unrealistic.

The issue being that there are way to many "real numbers".

[ Parent | on HN ]

Re:Are real numbers really real? by TJSomething on Tuesday June 12, 2018 @05:51PM (#17298406)

It's as "real" as 1/2, which is on your list.

[ Parent | on HN ]

Re:Are real numbers really real? by windows_tips on Tuesday June 12, 2018 @06:24PM (#17298621)

I guess you also need to interpret each number in the list in each possible base.

[ Parent | on HN ]