Dr. Discreto Riveros

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Sample prompts:

¿Por qué \( \sqrt{2} \) es irracional?

¿Puedes explicarme el Teorema de Cantor?

¿Cual es la base de teoría de conjuntos?

Demuestra que \( \left(\Sigma \models Q \right) \Longleftrightarrow \left(\forall \psi : \left(\bigwedge\limits_{i=1}^n {P_i \left(\psi\right) } \right) \rightarrow Q\left(\psi\right) \right) \)

¿Qué es la lógica proposicional?

Explícame consecuencia lógica en lógica de predicados.

Demuestre que para todo natural \( n>1 \) se cumple que \( 2! \cdot 4! \cdot 6! \cdot \ldots \cdot (2n)! \geq \left(\left(n+1\right)!\right)^n \)

Sean \( P=\{p, q, r, s, t, v\} \) ; \( \phi = \neg ( p \rightarrow q ) \lor (( r \lor s ) \rightarrow ( q \lor t )) \lor (\neg p \rightarrow \neg v ) \) una fórmula en \( L(P) \). Encuentre una fórmula \( \psi \) en CNF tal que \( \psi \equiv \phi \). Debe demostrar la equivalencia lógica.

¿Qué es la teoría de grafos?

¿Qué son las relaciones de equivalencia?

¿Cómo funcionan los algoritmos de búsqueda en árboles binarios?

¿Cómo se define una función biyectiva?

Generated by ChatGPT

Dr. Discreto Riveros is a GPT designed to function as an assistant in learning and understanding discrete mathematics. It can serve as an effective auxiliary tool for students and academics studying mathematics or related fields.

Using the capabilities of ChatGPT, it allows users to engage in detailed conversations about a multitude of math topics. This GPT provides an interactive way of exploring the fundamental concepts related to discrete mathematics.

Conversations can range from simple questions such as 'What is propositional logic?' to more complex prompts demanding proofs or demonstrations. With its diverse array of prompt starters, it integrates complex mathematical topics such as Cantor's Theorem, set theory, logical consequence in predicate logic, graph theory, equivalence relations, binary tree search algorithms, and the definition of a bijective function among others.

It encourages users to ask specific questions about propositions, which it then strives to answer in a comprehensive and understandable manner. The use of this GPT not only strengthens theoretical understanding but can also contribute to developing logical reasoning and problem-solving skills in the context of discrete mathematics.

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