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I have a number of questions involved here.

  1. What is a fraudulent transaction? Is there an example of this on the blockchain?

  2. Just to verify, in PoW the hashing algorithm is calculated to pass from one node to another and therefore there's no way that the transaction is fraudulent because otherwise the computation could not be completed, correct?

  3. How is staking coins doing the same verification process? What is the computation that occurs that verifies the tx? Also, how could a staked node verify a fraudlulent tx and then do the really lose their coins?

Sorry for all the questions combined, but they all lead me to better understand the first question I posed in title.

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  • What is a fraudulent transaction? Is there an example of this on the blockchain?

Good question. From my point of view, there is not because everyone needs to confirm its transactions, unless you gave your private key to someone you should not have (globally, never give your private key)

  • Just to verify, in PoW the hashing algorithm is calculated to pass from one node to another and therefore there's no way that the transaction is fraudulent because otherwise the computation could not be completed, correct?

This depend on your definition of fraudulent, but yes, this is correct.

  • How is staking coins doing the same verification process? What is the computation that occurs that verifies the tx? Also, how could a staked node verify a fraudlulent tx and then do the really lose their coins?

The process is exactly the same, except there is not difficulty, so your just hash it, broadcast it. If you are someone allowed to mine, then it is accepted. For your fraudulent stuff, still the same problem, what do you call a fraudulent tx? Because technically, this does not exists.

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  • To add to this, you can broadcast a block with any sort of invalid transactions in it you want. (I'm not sure the term "fraudulent" is useful here, but "invalid" has meaning. For example, you could have a transaction that transfers more ether than the sending account's balance.) Other participants in the network, however, validate the transactions in the block and reject a block that contains invalid transactions. So the block won't propagate very much, and a new block will end up getting mined and accepted instead. – user19510 Jan 15 '18 at 1:08
  • I'm not familiar yet with how PoS will work, but I think it's similar. In the PoW case, if you broadcast an invalid block, you miss out on the reward you could have gotten for mining a valid block. In the PoS case, I think you lose some ether that you've staked. – user19510 Jan 15 '18 at 1:10

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