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wiskunde: getallenleer: eigenschappen

1. Het vermenigvuldigen is commutatief in Q.
∀ a, b, c ∈ Q : (a %2b b) %2b c = a %2b (b %2b c) = a %2b b %2b c, ∀ a, b, c ∈ Q : (a . b) . c = a . (b . c) = a . b . c, ∀ a, b ∈ Q : a %2b b = b %2b a, ∀ a, b ∈ Q : a . b = b . a
2. Het optellen is associatief in Q.
∀ a, b ∈ Q : a %2b b = b %2b a, ∀ a, b ∈ Q : a . b = b . a, ∀ a, b, c ∈ Q : (a %2b b) %2b c = a %2b (b %2b c) = a %2b b %2b c, ∀ a, b, c ∈ Q : a . ( b %2b c ) = a . b %2b a . c = ( a %2b b ) . c = a . c %2b b . c
3. Het vermenigvuldigen is associatief in Q.
∀ a, b, c ∈ Q : (a . b) . c = a . (b . c) = a . b . c, ∀ a, b, c ∈ Q : (a %2b b) %2b c = a %2b (b %2b c) = a %2b b %2b c, ∀ a, b, c ∈ Q : a . ( b %2b c ) = a . b %2b a . c = ( a %2b b ) . c = a . c %2b b . c, ∀ a, b ∈ Q : a %2b b = b %2b a
4. ∀ a, b, c ∈ Q : a . ( b %2b c ) = a . b %2b a . c = ( a %2b b ) . c = a . c %2b b . c
∀ a, b, c ∈ Q : a . ( b %2b c ) = a . b %2b a . c = ( a %2b b ) . c = a . c %2b b . c, ∀ a, b ∈ Q : a %2b b = b %2b a, ∀ a, b, c ∈ Q : (a %2b b) %2b c = a %2b (b %2b c) = a %2b b %2b c, ∀ a, b, c ∈ Q : (a %2b b) %2b c = a %2b (b %2b c) = a %2b b %2b c