|Jul30-12, 07:58 PM||#1|
Currently working through Apostol need a check on my logic
1. The problem statement, all variables and given/known data
Prove the following theorem.
If a≠0, then (a-1)-1=a
Theorems proven before/axioms I am allowed to use:
Existence of reciprocals axiom: there exist real numbers x and y where x≠0 such that xy=1
Possibility of division Thm: basically a-1=1/a
2. Relevant equations
I just need a check on my proof since I am self studying the book. Any logical mistakes on my proof or suggestions etc? This is my first time writing proofs.
3. The attempt at a solution
Assume (a-1)-1=a is true.
Then by the existence of reciprocals axiom there exists an x such that (a-1)-1x=1.
ax=1Now by the possibility of division theorem we have,
x=1/a=a-1Finally since we assumed (a-1)-1=a was true it follows that:
It looks fine to me, I'm just a noob at proofs. Thanks.
|Jul30-12, 08:19 PM||#2|
Assume (a-1)-1=a is true.you're assuming that the thing you're proving is true.
That's a definite No-No .
I suggest starting with:
a-1 has a reciprocal, (a-1)-1.Now, multiply that by a, with a being on the right.
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