1. The Integers. 2. From the Integers to the Complex Numbers. 3. Polynomials. 4. Homomorphisms and Quotient Rings. 5. Field Extensions. 6. Groups. 7. Group Actions and Symmetry. 8. Non-Euclidean Geometries. Appendix A. A Logic Review, Sets and Functions, and Equivalence Relations. Appendix B. Miscellaneous Facts from Linear Algebra. Supplementary Reading. Table of Notations. Index.
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The purpose of this article is to introduce \textit. Let $\psi$ be a bijection from a nonempty set $G$ into another set $G^$, we prove that for any fixed operation on $G$, there exists a \textit operation on $G^$, where $\psi$ is an \textit. This finding allow us to show that we can make the set of natural numbers a \textit. Therefore we establish that the symmetric group $\mathcal_$ of a given nonempty set $G$ \textit on the set of all operations on $G$. Then we generalize the notions of $t$-norms, $t$-conorms and we give the equivalent of the $t$-conorm for \textit.
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Logic and Logical Philosophy
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