Page "Closed-form expression" Paragraph 11

Whether a number is a closed-form number is related to whether a number is transcendental.

Formally, Liouville numbers and elementary numbers contain the algebraic numbers, and they include some but not all transcendental numbers.

In contrast, EL numbers do not contain all algebraic numbers, but do include some transcendental numbers.

Closed-form numbers can be studied via transcendence theory, in which a major result is the Gelfond – Schneider theorem, and a major open question is Schanuel's conjecture.