General Discussion
In reply to the discussion: How would you answer this test question? From a 1st grade Common Core test. [View all]xocet
(4,348 posts)One takes 4 + 3 = 7 as given and the (implicit) definition of the additive group of integers:
1) 4 = 7 - 3
2) 3 = 7 - 4
3) 0 = 7 - (4 + 3) = 7 - 7
and then from the group definition
0 = k + (-k), for all k that are integers
becomes
0 = k - k, for all integers k, which could be interpreted as a subtraction sentence.
Can one not argue that once one has the identity element of the group from the original sentence one can extend the initial equation to the whole of the group of integers?
If so, then would it be proper to say that the equation 4 + 3 = 7 is equivalent to a countable infinity of subtraction sentences via the identity axiom?
As far as I know, this is correct, but it has been a while, so I would definitely be interested in your thoughts on the above argument.