MHB How Do You Solve the Second Part of an Equivalence Relations Problem?

Thread starter loydchase
Start date Nov 17, 2018
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Equivalence Equivalence relations Relations

Nov 17, 2018

loydchase

I understand that the first part of the equation is an equivalence class due to reflexivity, symmetry, and transivity... but I am confused on the second part. Could someone please help me out? THANKS

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Nov 17, 2018

Evgeny.Makarov

Gold Member

MHB

Welcome to the forum!

What exactly is the problem statement?

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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