I am trying to understand what problem in bitcoin proof of work solves and came to this somewhat helpful quote:
So, for instance, if a miner controls one percent of the computing power being used to validate Bitcoin transactions, then they have roughly a one percent chance of winning the competition. So provided a lot of computing power is being brought to bear on the competition, a dishonest miner is likely to have only a relatively small chance to corrupt the validation process, unless they expend a huge amount of computing resources.
Does this mean that proof of work prevents say double spending because of following reasons. Imagine attacker introduces 100000 rogue nodes in the network and their goal is to send false information about transaction validity - but since these nodes need to do proof of work, in total, when all 100000 nodes are doing proof of work this is too costly for attacker. Is that right? So because of this proof of work keeps attackers at bay.