How to/Can we show irrational numbers?

Layton Park

Layton Park

Answered question

2022-11-06

How to/Can we show irrational numbers?

Answer & Explanation

Stella Andrade

Stella Andrade

Beginner2022-11-07Added 19 answers

A real number a is irrational iff its decimal (or binary) expansion doesn't become ultimately periodic. You can formulate this in the following way:
a = a 0 . a 1 a 2 a 3 ( a 0 Z ,   a k { 0 , 1 , , 9 }   ( k 1 ) )
is irrational if p N 1 , n N 1 there is a k > n with a k a k + p .

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