- #1
C0nfused
- 139
- 0
Hi everybody,
This may have been discussed before ( and by me) but I would like to see a proof of the following statement:
" (ab)+(ac)=ab+ac"
Ok let me explain a bit. When we want to set some axioms about the real numbers we say that we define two functions from RxR->R, addition(+) and multiplication, with the following properties:
...etc... a(b+c)=ab+ac...etc
Does the above imply that multiplication precedes addition? I mean, we define how parentheses are used, but only by looking in the above property we can assume that multiplication precedes addition and that it's the same writing ab+ac and
(ab)+(ac)? Some have told me that the order of operations is simply a convention, that there's not much relationship with the axioms of algebra and that it could have been done in another way. But i think that almost anything,including the order of operations, can be derived from the axioms. A proof could be to interprete the right-hand side expression in all possible ways and see with examples that it's not equal to the left-hand side expression, but i think there must be another one,more formal.
Sorry for saying so much about this. Hope u won't find it as stupid as it sounds at first...
Thanks
This may have been discussed before ( and by me) but I would like to see a proof of the following statement:
" (ab)+(ac)=ab+ac"
Ok let me explain a bit. When we want to set some axioms about the real numbers we say that we define two functions from RxR->R, addition(+) and multiplication, with the following properties:
...etc... a(b+c)=ab+ac...etc
Does the above imply that multiplication precedes addition? I mean, we define how parentheses are used, but only by looking in the above property we can assume that multiplication precedes addition and that it's the same writing ab+ac and
(ab)+(ac)? Some have told me that the order of operations is simply a convention, that there's not much relationship with the axioms of algebra and that it could have been done in another way. But i think that almost anything,including the order of operations, can be derived from the axioms. A proof could be to interprete the right-hand side expression in all possible ways and see with examples that it's not equal to the left-hand side expression, but i think there must be another one,more formal.
Sorry for saying so much about this. Hope u won't find it as stupid as it sounds at first...
Thanks
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