We have proposed a system for electronic transactions without relying on trust. We started with the usual framework of coins made from digital signatures, which provides strong control of ownership, but is incomplete without a way to prevent double-spending. To solve this, we proposed a peer-to-peer network using proof-of-work to record a public history of transactions that quickly becomes computationally impractical for an attacker to change if honest nodes control a majority of CPU power.
You forgot the "Conclusion" part of Bitcoin's whitepaper, Bitcoin only has a "proposed solution" for double-spending but was never guaranteed by Saotoshi himself aside from that Satoshi is also aware that a 51% attack is possible that is why he is talking about PoW on transactions on how should it be "computationally impractical" so that it would be "impractical" for an attacker to infiltrate the network. But Satoshi didn't even dived in to the possibility of a 51% attack from happening in Bitcoin's network, I know it would require a lot of resources for an individual or a group to pull through and control 51% of the hash rate but if we are only talking about the chances of this happening I know we all know that a 51% attack has a chance to happen.