Proof ios stake or proof of work

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Proof ios stake or proof of work
I have extracted a section of the tutorial as below: 
"In a Proof of Stake system, this risk can be mitigated.

Suppose malicious miner Alice wants to mine on the red chain. Even if she dedicates all of her hash power to it, she won’t get any other miner to join her on the new chain. Everyone else will still continue to mine on the blue chain because it is more profitable and risk-free to mine on the longer chain" 

Is above proof of stake of Proof of Work system?

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Hi Yew,

It is proof of stake. In case of proof of work, she would need about 51% of hash power to initiate and continue mining on the long chain. If Alice could generate that much hash power on her own (say using advanced hardware etc.), the red chain would become dominant, theoretically speaking. Whereas, in case of proof of stake, no matter how much hash power Alice puts to use, she won’t be able to initiate and incentivize miners to join in. The reason being, for a PoS based blockchain, you need stakes in terms of ETH to be able to add/validate a block which is not the same as aggregating computational power. Furthermore, the staked ETH would be lost in case of malicious attempts creating an incentive for validators to avoid validating incorrect transactions. To summarize, staked ETH > ETH earned through transaction reversal/invalid transaction.

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