What are reals?

Some articles on real, reals:

Hasse Principle - Intuition
... if it has rational solution, then this also yields a real solution and a p-adic solution, as the rationals embed in the reals and p-adics a global ... is when can you patch together solutions over the reals and p-adics to yield a solution over the rationals when can local solutions be joined to form a global solution? One can ask this for other ... For number fields, rather than reals and p-adics, one uses complex embeddings and -adics, for prime ideals ...
Lee–Yang Theorem - Statement - Preliminaries
... to be ferromagnetic if all the coefficients in the interaction term Jjk are non-negative reals ... The partition function is given by where each dμj is an even measure on the reals R decreasing at infinity so fast that all Gaussian functions are integrable, i.e A rapidly decreasing ...
Determinator - Consequences of Determinacy - Regularity Properties For Sets of Reals
... pointclass such that every game in Γ is determined, then every set of reals in Γ has the property of Baire ... Γ (for Γ with sufficient closure properties) implies that every set of reals that is the projection of a set in Γ has the property of Baire ... of a measurable cardinal implies Π11 determinacy, which in turn implies that every Σ12 set of reals has the property of Baire ...
Set Notation - Focusing On The Membership of A Set
... to the braces notation is used to express intervals on the real line ... interval is well defined only because the real numbers are totally ordered ... unit interval, for instance, is the set of reals between 0 and 1 (inclusive) ...
Constraint Logic Programming - Terms and Constraints - Reals
... Constraint logic programming with real numbers uses real expressions as terms ... symbols are used, terms are expressions over reals, possibly including variables ... In this case, each variable can only take a real number as a value ...