Is there an explicit irrational number which is not known

Dale Tate

Dale Tate

Answered question

2022-06-23

Is there an explicit irrational number which is not known to be either algebraic or transcendental?

Answer & Explanation

Rebekah Zimmerman

Rebekah Zimmerman

Beginner2022-06-24Added 32 answers

Maybe the best-known example is Apery's constant,
ζ ( 3 ) = n = 1 1 n 3 = 1.20205 ,
which Apery proved was irrational a few decades ago; this result is known as Apery's Theorem.
By contrast, ζ ( 2 ) = n = 1 1 n 2 has value π 2 6 , which is transcendental because π is.

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