1. Just One Last ?

Thank you soooooooo muchhhhh Captainblack. Without you, I won't be able to prove these laws of algebra. I have ONE LAST prove I can't prove. Will you pleaseeee helpp me on this one too? The axioms are still needed to prove this problem as well.

For every natural number i, for every natural number j, for every natural number k, i(j + k) = ij + ik.

2. Originally Posted by jenjen
Thank you soooooooo muchhhhh Captainblack.
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Do you let me prove instead,
$(j+k)i=(ji)+(ki)$?--->Because CaptainBlank shown it was commutative.
If yes, then I have a prove (involving induction axiom) which I will post tomorrow because it is late here.

3. Originally Posted by jenjen
Thank you soooooooo muchhhhh Captainblack. Without you, I won't be able to prove these laws of algebra. I have ONE LAST prove I can't prove. Will you pleaseeee helpp me on this one too? The axioms are still needed to prove this problem as well.

For every natural number i, for every natural number j, for every natural number k, i(j + k) = ij + ik.
The first seven pages of this pdf document provideds the proofs of the basic
properties of arithmetic for Peano Arithmetic. Though with a slightly different
notation you can find the basic ideas needed to prove all the properties you

RonL

4. Thanks to you to ThePerfectHacker !!! of course!!