MHB Equivalences and Partitions and Properties of binary relations

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The discussion centers on a request for assistance with questions about equivalences, partitions, and properties of binary relations. The response emphasizes the importance of adhering to forum rules, particularly regarding the number of questions allowed per thread. Rule 8 specifically limits users to two questions, while the original post included twenty. Participants are encouraged to familiarize themselves with the forum's guidelines to ensure productive interactions. Following the rules will enhance the likelihood of receiving help effectively.
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If someone could explain some of the steps needed to work out these 2 questions it would be much appreciated!

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Hello, sadsadsadsa!

We would be glad to help, but you should study the http://mathhelpboards.com/rules/ first. On the rules page, click on the Expand button in the top-left corner. In particular, read rules 8, 11 and 6. Thus, rule 8 asks not to ask more than two questions in a thread, while you posted 20 questions in total.
 

Thread 'Value of intuitionistic logic'

I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
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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...
View full post »

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