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You are not logged in. #1 20130217 16:35:06
Properties of additionI have a younger cousin who wants to know how to prove addition is commutative and associative for whole numbers .but i don't know how to do that,can anyone help?plus it'd be good if anyone can tell me how the proof is extended to other number sets. Last edited by {7/3} (20130217 16:38:06) There are 10 kinds of people in the world,people who understand binary and people who don't. #2 20130217 20:31:46
Re: Properties of additionHi The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #3 20130218 10:49:20
Re: Properties of additionHi! Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #4 20130218 13:58:38
Re: Properties of additionNever mind i found ways to prove commutative and associative law of addition of natural numbers in internet[though i'd appreciate it if anyone tells me how this is extended to Z,Q,R,..] There are 10 kinds of people in the world,people who understand binary and people who don't. #5 20130218 23:08:02
Re: Properties of addition
It depends on how you are defining your sets of numbers. If you are defining them by axioms, then there is nothing to prove since the axioms will include commutativity and associativity of addition. But if you are constructing them from smaller sets of numbers, then commutativity and associativity need to be proved. For example, here is briefly how is constructed from . Define a relation on by iff . (Hint: Think of as the "difference" .) Then is an equivalence relation and is defined as the set of all equivalence classes under . Let the equivalence class containing be denoted . Then addition in is defined as After checking that the operation is well defined, one can proceed to verify that is commutative and associative. Moreover, zero in is the equivalence class and multiplication in is defined as . Similarly can be constructed from as equivalence classes of the equivalence relation on defined by iff . Letting the equivalence class containing be denoted addition in is definied as Last edited by scientia (20130218 23:19:54) #7 20130219 00:18:00
Re: Properties of addition
No, is constructed by means of either Dedekind cuts or equivalence classes of Cauchy sequences of rationals. The process is very different and much more complicated because you are now constructing an uncountable set from a countable one.
#8 20130219 05:17:58
Re: Properties of additionI think I've seen that before, but, then it seems that N is not a subset of Z. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment 