The real numbers logic language is the set of all well-formed closed formulas written with the following
symbols :- rational numbers;
- real number operators : +, ×
- comparaison operators : =, >, <, ≤, ≥
- boolean operators : and, or, not, →
- universal and existential quantifiers : ∀, ∃
- ∃x, x² + 5x + 2 = 0. - ∀x, (x>0 → ∃y, x = y²). Deciding if such a formula is true is decidable. |

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This explaination looks like a gamebook. :)

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Bibliography: this gamebook is inspired by the Chapter 1, paragraph 3 from "Foundations of Mathematics" from Erwin Engeler, edition Springer-Verlag.