Formal Sciences

Mathematics Core

Math facts — equations, proofs, and number patterns from classic books.

Where the facts come from

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#math_001 · unison_mathematics_core

Logic De Morgan laws: ¬(A∧B)≡¬A∨¬B; ¬(A∨B)≡¬A∧¬B. Modus ponens: [P∧(P→Q)]→Q. Modus tollens: [¬Q∧(P→Q)]→¬P. Contrapositive: (P→Q)≡(¬Q→¬P).

#math_002 · unison_mathematics_core

Calculus Taylor series: f(x)=Σ[f^(n)(a)/n!](x-a)^n. e^x=1+x+x²/2!+x³/3!+… sin(x)=x-x³/3!+x⁵/5!-… Radius convergence: lim|a_{n+1}/a_n|.