Can we represent pi as a dedeking cut in the rationals

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The discussion centers on the representation of the mathematical constant pi as a Dedekind cut in the rationals. The user initially inquires whether pi can be expressed similarly to how √2 is represented as the set of rationals {x ∈ Q : x² < 2}. They reference the concept that not all reals can be defined, questioning the specific Dedekind cut representation for pi. Ultimately, the user found the answer in another thread and requested the closure of this discussion.

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  • Familiarity with the construction of real numbers from rational numbers
  • Basic knowledge of irrational numbers, specifically pi
  • Concept of sets and their representations in mathematics
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Hi , I only recently read the construction of reals from rationals.

I could grasp that [itex]\sqrt{2}[/itex] can be represented as the set of rationals given by
{x[itex]\in[/itex] Q : x2 < 2 } . As we know this set is defined purely in terms of Q.

Is there a dedekind cut representation for pi as well ?

I read somehwhere that not all reals can be defined. But since pi is defined , what would it's dedeking cut representation be?
 
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