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(-a)b = a(-b) = -(ab) (Proof) [ILIEKMATHPHYSICS]
|a| - |b| ≤ |a - b| (Proof) [ILIEKMATHPHYSICS]
Prove for positive integers a and b, if a ﹥ b then a - b is a positive integer (ILIEKMATHPHYSICS)
Prove that ab = gcd(a,b) ⋅ lcm(a,b) for positive integers a and b [ILIEKMATHPHYSICS]
|a + b| ≤ |a| + |b| (Proof) [ILIEKMATHPHYSICS]
||a| - |b|| ≤ |a - b| (Proof) [ILIEKMATHPHYSICS]
Prove that (1/a)(1/b) = 1/ab [ILIEKMATHPHYSICS]
Prove if a prime p divides ab, then p divides a or b (ILIEKMATHPHYSICS)
Prove that |A ∪ B| = |A| + |B| for finite disjoint A and B (ILIEKMATHPHYSICS)
-(a-b) = b-a (Proof) [ILIEKMATHPHYSICS]
Prove that -(a - b) = b - a (Second Proof) (ILIEKMATHPHYSICS)
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Last Updated: August 18, 2026
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![|ab| = |a||b| (Proof) [ILIEKMATHPHYSICS] Guide](https://i.ytimg.com/vi/zFa2ORKuFoU/mqdefault.jpg)
![Details |a + b| = |a| + |b| iff ab ≥ 0 (Proof) [ILIEKMATHPHYSICS] Update](https://i.ytimg.com/vi/SRr8JlcD74w/mqdefault.jpg)
![Full (-a)(-b) = ab (Proof) [ILIEKMATHPHYSICS] Guide](https://i.ytimg.com/vi/beve44xi2U8/mqdefault.jpg)
![(-a)b = a(-b) = -(ab) (Proof) [ILIEKMATHPHYSICS]](https://i.ytimg.com/vi/OrwgzrMxkO8/mqdefault.jpg)
![|a| - |b| ≤ |a - b| (Proof) [ILIEKMATHPHYSICS]](https://i.ytimg.com/vi/MyNhQVzMcVQ/mqdefault.jpg)
![Prove that ab = gcd(a,b) ⋅ lcm(a,b) for positive integers a and b [ILIEKMATHPHYSICS]](https://i.ytimg.com/vi/HAw-loc8zn0/mqdefault.jpg)
![|a + b| ≤ |a| + |b| (Proof) [ILIEKMATHPHYSICS]](https://i.ytimg.com/vi/oILZEmcSZ7s/mqdefault.jpg)
![||a| - |b|| ≤ |a - b| (Proof) [ILIEKMATHPHYSICS]](https://i.ytimg.com/vi/Mc_BxgijKM0/mqdefault.jpg)
![Prove that (1/a)(1/b) = 1/ab [ILIEKMATHPHYSICS]](https://i.ytimg.com/vi/4bGRzhKSfYU/mqdefault.jpg)
![-(a-b) = b-a (Proof) [ILIEKMATHPHYSICS]](https://i.ytimg.com/vi/NchD4cUT1k8/mqdefault.jpg)
![If a ≤ b and b ≤ a, then a = b (Proof) [ILIEKMATHPHYSICS] Guide](https://i.ytimg.com/vi/3LZVA03jApQ/mqdefault.jpg)
