Kabbalist

Let A,B,C,K be natural numbers. Let T signify true. Let F signify false. So we have ∀K(K≤2→∃A,B,C(A^K+B^K=C^K ))=T. But this is equivalent to ∀K(K>2∨∃A,B,C(A^K+B^K=C^K ))=T. By the principle of duality we then have…

In Category theory, can the dual of the implication A→B be its converse, which is B→A?

Couldn’t the implication sign “→” in A→B be viewed as a morphism between A and B? Also, could mathematical operators like plus, minus, AND, OR, etc. be viewed as morphisms?

This is a corrected version of Maths where the Pythagorean Triples Don’t Exist. Let A,B,C, and K be elements of the natural numbers. 1. ∀K(K≤1∧∃A,B,C(A^K+B^K=C^K )) 2. ∀K(∃A,B,C(A^K+B^K=C^K )∧K≤1) 3.…

Are there maths that violate Fermat’s Last Theorem? I ask because of the following. Let A,B,C, and K be elements of the natural numbers. 1. ∃A,B,C,K(K≤2∧A^K+B^K=C^K ) 2. ∃A,B,C,K(K≤2∨A^K+B^K=C^K ) 3.…

Let A be the set of prime numbers. Let B_1 and B_2 be subsets of A. Let C be an element of A Let F(X) signify that X is finite. Let I(X) signify that X is infinite. 1. ∃B_1 (F(B_1 )) 2. ∃B_2∃C(C∉B_2 ) 3. ∃B_1 (F(B_1…

∀A,B,C,K_1,K_2∈N. By this I mean they are all elements of the natural numbers. 1. ∃K_1 (K_1≤1) 2. ∃A,B,C,K_2 (A^(K_2 )+B^(K_2 )=C^(K_2 ) ) 3. ∃K_1 (K_1≤1)∧∃A,B,C,K_2 (A^(K_2 )+B^(K_2 )=C^(K_2 ) ) 4. ∃A,B,C,K_2 (A^(K_2…

Is the following valid? Let ∀A,B,C,K_1,K_2∈N. By this I mean they are all elements of the natural numbers. 1. ∃K_1 (K_1≤1) 2. ∃A,B,C,K_2 (A^(K_2 )+B^(K_2 )=C^(K_2 ) ) 3. ∃K_1 (K_1≤1)∧∃A,B,C,K_2 (A^(K_2 )+B^(K_2 )=C^(K_2…

Are there maths where the Pythagorean triples don’t exist? I ask because of the following: Let A,B,C, and K be elements of the Natural Numbers 1.∃K(K≤1)∧∃A,B,C(A^K+B^K=C^K ) 2.∃A,B,C(A^K+B^K=C^K )∧∃K(K≤1)…