- #1
Werg22
- 1,427
- 1
I was asked to find a paper with proofs on the basis of arthimetics. For example proof that the product of a serie of factors is the same no matter what is the order the're read, and other arthimetic rules.
fourier jr said:what you're talking about is associativity. i think any book on abstract algebra would have what you're looking for.
shmoe said:You know, I don't think I could name one. You'll usually get something like "using induction and the associativity law, we can unambiguously write multiplications without brackets," but I can't recall ever seeing it worked out in full gory detail.
shmoe said:I know it can be done, I just can't recall ever seeing it in an abstract algebra book. It's usually waffled over though and with good reason-it's not really difficult or enlightening, just messy.
JasonRox said:I don't see why it should though. You talk about associativity, but that's if groups have that property, which is what you must show yourself.
shmoe said:groups are all associative, it's part of the definition of a group.
DeadWolfe said:I might be remembering wrong, but doesn't Spivak's Calculus start with some of this stuff?
Werg22 said:As a matter of fact I did but I was never skilled in the area of research. Thanks alot!
Werg22 said:HallsofIvy, I lack the proper knowledge to understand your paper. Is the proof of these axioms absolutly require basis in Number Theory?
Werg22 said:HallsofIvy, I lack the proper knowledge to understand your paper. Is the proof of these axioms absolutly require basis in Number Theory?
fourier jr said:maybe i'm too fast for my own good. iit isn't just associativity??
fourier jr said:maybe i'm too fast for my own good. iit isn't just associativity??
Werg22 said:I found a way to proove it somehow by induction.
It is easy to proove those identities:
1. [tex]ab=ba[/tex]
2.[tex]abc=(ab)c=a(bc)[/tex]
Then we can proove that for this special case (3 elements) the order dosen't matter. Thus for 4 elements;
[tex]abcd = (abc)d [/tex] By definition .
Now we can proove tha not matter what the order in the parenthesis, the result remains unchanged. The proove the general case, we have to proove that you can place any of the element to any wished position without chaging the result. By property 1, d can be the first element and the last. It is easy to see that any number can be put first, and since there is 3 remaining elements, and we already prooved it can be arranged a wished, then any combination can be formed with those elements without changing the result. Then we prooved this for 4 elements, and we proove it for 5 the same way.
Q.E.D.?