# All pages (Claim namespace)

From CS2800 wiki

- Claim:2 is prime
- Claim:A/R partitions A
- Claim:A = (A ∩ B) ∪ (A ∖ B)
- Claim:A ∩ (B 1 ∪ ... ∪ B n) ⊆ (A ∩ B 1) ∪ ... ∪ (A ∩ B n)
- Claim:A ∩ (B∪C) ⊆ (A∩B) ∪ (A∩C)
- Claim:A ∩ B ⊆ A
- Claim:A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
- Claim:Base b representation
- Claim:Bayes' rule
- Claim:Bijections have two-sided inverses
- Claim:Bézout coefficients exist
- Claim:Cantor-Schroeder-Bernstein theorem
- Claim:Cardinality of evens
- Claim:Cardinality of the integers
- Claim:Conditional probabilities satisfy Kolmogorov's axioms
- Claim:Euclidean division algorithm
- Claim:Every natural number has a prime factorization
- Claim:Functions with left inverses are injective
- Claim:Functions with right inverses are surjective
- Claim:Functions with two-sided inverses are bijective
- Claim:Gcd(a,b) is a common divisor of a and b
- Claim:Gcd(a,b) is greater than all other common divisors of a and b
- Claim:Giving probabilities for simple outcomes is enough
- Claim:If A ⊆ B and B is countable then A is countable
- Claim:If A ⊆ B then A ∩ B = A
- Claim:If A ⊆ B then A ∩ C ⊆ B ∩ C
- Claim:If p is prime, then φ(p) = p - 1
- Claim:Injections have left inverses
- Claim:Law of total probability
- Claim:Limit of x at 0 is 0
- Claim:Limit of x at 0 is not 1
- Claim:Pr(E) ≤ 1
- Claim:Pr(S ∖ E) = 1 - Pr(E)
- Claim:Random variables satisfy distributivity
- Claim:Strong induction is equivalent to weak induction
- Claim:Surjections have right inverses
- Claim:The base b representation is unique
- Claim:The power set of the naturals is uncountable
- Claim:The quotient and remainder are unique
- Claim:The set of reals is uncountable
- Claim:There is a unique function with an empty domain
- Claim:There is no function with an empty codomain
- Claim:Two definitions of independence are equivalent
- Claim:Union computation
- Claim:Weak induction principle starting at k is equivalent to weak induction
- Claim:Weak induction principle with n-1 is equivalent to weak induction
- Claim:Σi = n(n+1)/2
- Claim:∅ ∉ ∅
- Claim:∅ ⊆ A
- Claim:≤ and ≥ are related
- Claim:≤ is reflexive
- Claim:≤ is transitive
- Claim:⊆ implies ≤
- Claim:⊆ is transitive
- Claim:│ℕ ∪ -1│ = │ℕ│
- Claim:│ℕ ⨯ ℕ│ = │ℕ│
- Claim:⟦a⟧=⟦b⟧ if and only if aRb
- Claim:⟦a⟧ is a unit mod m if and only if gcd(a,m) = 1
- Claim:⟦k⟧ m is a unit if and only if gcd(k,m) = 1