Answers

2014-06-29T13:20:10+05:30
The product of cardinals comes from the cartesian product.κ·0 = 0·κ = 0.κ·μ = 0 → (κ = 0 or μ = 0).
One is a multiplicative identity κ·1 = 1·κ = κ.
Multiplication is associative (κ·μ)·ν = κ·(μ·ν).
Multiplication is commutative κ·μ = μ·κ.
Multiplication is non-decreasing in both arguments: κ ≤ μ → (κ·ν ≤ μ·ν and ν·κ ≤ ν·μ).
Multiplication distributes over addition: κ·(μ + ν) = κ·μ + κ·ν and (μ + ν)·κ = μ·κ + ν·κ.
Assuming the axiom of choice, multiplication of infinite cardinal numbers is also easy.
 If either κ or μ is infinite and both are non-zero, then
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  • Brainly User
2014-06-29T13:50:11+05:30
The number of distinct elements in a finite set is called product of cardinal number.
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