Is ( ( (

Alisa Durham

Alisa Durham

Answered question

2022-05-15

Is ( ( ( 2 ) 2 ) 2 ) an irrational number?

Answer & Explanation

stafninumfu1tf

stafninumfu1tf

Beginner2022-05-16Added 18 answers

Your number is not finite. Let x 0 = 2 and x n + 1 = x n 2 for all n Z 0 .
Then x n 2 . Proof: x 0 = 2 and x k 2 means x k 2 > x k 2 .
Assume for contradiction your number is finite, i.e. lim n x n := L is finite.
( ( ( 2 ) 2 ) 2 ) = lim n x n L = lim n ( ( x n 2 ) 2 )
= lim n ( x n x n ) = L L
L = L 2 L { 0 , 1 }
Impossible, since x n 2 .

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