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Additive inverses are unique in any ring. The subtle things I skipped over because of the technicalities involved is how do I know the distributive property ho
by yequalsx 14y ago
Additive inverses are unique in any ring. The subtle things I skipped over because of the technicalities involved is how do I know the distributive property holds for negative integers. Indeed, what is a negative integer? How does one get them from the natural numbers? Suffice it to say that this can all be defined in a consistent, precise way and everything works out.
- gizmo686 14y agoActually, we only think that it can be described in a consistent way. We have proven it consistent using set theory , but Godwell's theorems tell us that we cannot prove a system to be consistent without using something outside of said system (unless the system is inconsistent). This means that there is some level in our chain of proofs that cannot be proven consistent.
- deleted 14y ago[deleted]