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Precalc Craziness 1
Some crazy equation sorts and such and such
Question | Answer |
---|---|
(N,+) | Abelian Monoid |
(N, x) | Abelian Monoid |
(Z, +) | Abelian Group |
(Z, x) | Abelian Monoid |
(Q, +) | Abelian Group |
(Q^x, x) | Abelian Group |
(Q^q, o) | Monoid |
(Q^q, +) | Abelian Group |
(Q^q, x) | Abelian Monoid |
(P, o) | Monoid |
(P, +) | Abelian Group |
(P, x) | Abelian Monoid |
(A^o, o) | Group |
(A, +) | Abelian Group |
(A, x) | Nothing |
What is necessary to be a Monoid? | Closure, Associativity and Identity |
What is necessary to be a Group? | Closure, Associativity, Identity and Inverses |
What is necessary to be Abelian? | Commutative Property |
What does superscript "o" stand for in (A^o, o)? | It means you have to take out the constant functions or else the functions won't have inverses (because no matter what your input is in f(x)=5, the answer will be 5, not the ID) |
What does superscript "x" stand for in (Q^x, x)? | It means you have to take zero out of the set of rational numbers, because it doesn't have an inverse. |