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Proof of the Mathematical Induction Principle (ILIEKMATHPHYSICS)
ILIEKMATHPHYSICS
18 พ.ค. 2024
การดู 1,023 ครั้ง
0+1+2+...+n equals n(n+1)/2 Proof [ILIEKMATHPHYSICS]
If B ⊆ Z+ is infinite, then there is a bijection f : Z+ → B (Proof) [ILIEKMATHPHYSICS]
(A\B) ∪ B = A iff B ⊆ A (Proof)
If A is finite, then A ~ B iff B is finite and |A| = |B| (Proof) [ILIEKMATHPHYSICS]
Proof that n + (m++) = (n + m)++ for all natural numbers n and m (ILIEKMATHPHYSICS)
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c(a1 + a2 + ... + an) = ca1 + ca2 + ... + can (Proof) [ILIEKMATHPHYSICS]
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If A ∪ C = B ∪ C, A ∩ C = ∅, and B ∩ C = ∅, then A = B (Proof)
Proof that a sum can be partitioned into a sum of sums (ILIEKMATHPHYSICS)
If A is countable and A ~ B, then B is countable (Proof) [ILIEKMATHPHYSICS]
If f is injective, then f↾C is injective (Proof) [ILIEKMATHPHYSICS]
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Proof For The Formula For Sum of n Integers
Proof that n + 0 = n for all natural numbers n (ILIEKMATHPHYSICS)
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