Axioms Word Scramble
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Term | Definition |
Closure Axiom for Addition | a+b is a unique real number |
Associative Axiom for Addition | (a+b)+c=a+(b+c) |
Commutative Axiom for Addition | a+b=b+a |
Identity Axiom for Addition | There exists an element 0∈R such that for each a∈R, 0+a=a and a+0=a |
Axiom of Additive Inverses | There exists an element -a∈R for each a∈R, such that a+(-a)=0 and (-a)+a=0 |
Closure Axiom for Multiplication | ab is a unique real number |
Associative Axiom for Multiplication | (ab)c=a(bc) |
Commutative Axiom for Multiplication | ab=ba |
Identity Axiom for Multipication | There exists an element 1∈R, 1≠0, such that for each a∈R, a·1=a and 1·a=a. |
Axiom of Multiplicative Inverses | There exists an element 1/a∈R for each nonzero a∈R such that 1/a·a=1 and a·1/a=1 |
Distributive Axiom of Multiplication with Respect to Addition | a(b+c)=ab+bc and (b+c)a=ba+ca |
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