Use of proof of work in bitcoin 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.
Imagine attacker introduces 100000 rogue nodes in the network and their goal is to send false information about transaction validity ...


That's no possible. Every node validates blocks and transactions for itself. It doesn't matter what another node tries to represent - if the block is invalid, it's ignored by the receiving node.

Proof-of-work is unnecessary for determining block validity.

What proof-of-work does do is makes block generation expensive. Without it, nodes could generate blocks cheaply, rolling back transaction history by publishing replacements for previous blocks willy-nilly.

To rewrite a previous block, a node must not only rewrite the block its self, but all of its descendants. It must re-do all of the work that was previously done.

To re-iterate: nodes validate transactions and blocks for themselves. Proof-of-work doesn't convince nodes of block validity. It convinces them that a certain amount of work must have been performed to produce the block.

A node uses the cumulative proof-of-work when faced with a choice of two or more valid block chains. The one with the most proof-of-work is used to build the global transaction log.