Fix typos in chapter 1.

01_introduction.asciidoc

@@ -27,7 +27,7 @@ Hash function:: ((("hash function, defined")))A cryptographic hash function is a
 
 Node:: ((("node, defined")))A computer that participates in a network. A Lightning node is a computer that participates in the Lightning Network. A Bitcoin node is a computer that participates in the Bitcoin network. Typically an LN user will run a Lightning node _and_ a Bitcoin node.
 
-On-chain versus off-chain:: ((("on-chain payment","defined")))A payment is _on-chain_ if it is recorded as a transaction on the Bitcoin (or other underlying) blockchain. ((("off-chain payment")))Payments sent via payment channels between Lightning nodes, and which are not visible in the underlying blockchain, are called _off-chain_ payments. Usually in the Lightning Network, the only on-chain transactions are those used to open and close a Lightning payment channel. A third type of channel modifying transaction exists, called splicing, which can be used to add/remove the amount of funds committed in a channel.
+On-chain versus off-chain:: ((("on-chain payment","defined")))A payment is _on-chain_ if it is recorded as a transaction on the Bitcoin (or other underlying) blockchain. ((("off-chain payment")))Payments sent via payment channels between Lightning nodes, and which are not visible in the underlying blockchain, are called _off-chain_ payments. Usually in the Lightning Network, the only on-chain transactions are those used to open and close a Lightning payment channel. A third type of channel-modifying transaction exists, called splicing, which can be used to add/remove the amount of funds committed in a channel.
 
 Payment:: ((("payment","defined")))When value is exchanged on the Lightning Network, we call this a "payment" as compared to a "transaction" on the Bitcoin blockchain.
 
@@ -66,7 +66,7 @@ Before we get into how the Lightning Network works, it's important to understand
 
 In broad terms, there are a handful of ways to ensure fair outcomes in interactions between individuals who may have competing interests:
 
-Require trust:: You only interact with people whom you already trust, due to prior interactions, reputation, or familial relationships. This works well enough at small scale, especially within families and small groups, that it is the most common basis for cooperative behavior. Unfortunately, it doesn't scale and it suffers from tribalist (in-group) bias.
+Require trust:: You only interact with people whom you already trust, due to prior interactions, reputation, or familial relationships. This works well enough at small scale, especially within families and small groups, and is the most common basis for cooperative behavior. Unfortunately, it doesn't scale and it suffers from tribalist (in-group) bias.
 
 Rule of law:: Establish rules for interactions that are enforced by an institution. This scales better, but it cannot scale globally due to differences in customs and traditions, as well as the inability to scale the institutions of enforcement. One nasty side effect of this solution is that the institutions become more and more powerful as they get bigger and that may lead to corruption.
 
@@ -123,7 +123,7 @@ Now that you understand this basic pattern, you will start seeing it everywhere
 
 ==== Example of the Fairness Protocol
 
-((("fairness protocol","Proof of Work example")))((("PoW (Proof of Work) algorithm")))((("Proof of Work (PoW) algorithm")))The most prominent example of a fairness protocol is Bitcoin's consensus algorithm, Proof of Work (PoW). In Bitcoin, miners compete to verify transactions and aggregate them in blocks. To ensure that the miners do not cheat, without entrusting them with authority, Bitcoin uses a system of incentives and disincentives. Miners have to use electricity and dedicate hardware doing "work" that is embedded as a "proof" inside every block. This is achieved because of a property of hash functions where the output value is randomly distributed across the entire range of possible outputs. If miners succeed in producing a valid block fast enough, they are rewarded by earning the block reward for that block. Forcing miners to use a lot of electricity before the network considers their block means that they have an incentive to correctly validate the transactions in the block. If they cheat or make any kind of mistake, their block is rejected and the electricity they used to "prove" it is wasted. No one needs to force miners to produce valid blocks; the reward and punishment incentivize them to do so. All the protocol needs to do is ensure that only valid blocks with Proof of Work are accepted.
+((("fairness protocol","Proof of Work example")))((("PoW (Proof of Work) algorithm")))((("Proof of Work (PoW) algorithm")))The most prominent example of a fairness protocol is Bitcoin's consensus algorithm, Proof of Work (PoW). In Bitcoin, miners compete to verify transactions and aggregate them in blocks. To ensure that the miners do not cheat, without entrusting them with authority, Bitcoin uses a system of incentives and disincentives. Miners have to use electricity and dedicate hardware towards "work" that is embedded as a "proof" inside every block. This is achieved because of a property of hash functions where the output value is randomly distributed across the entire range of possible outputs. If miners succeed in producing a valid block fast enough, they are rewarded by earning the block reward for that block. Forcing miners to use a lot of electricity before the network considers their block means that they have an incentive to correctly validate the transactions in the block. If they cheat or make any kind of mistake, their block is rejected and the electricity they used to "prove" it is wasted. No one needs to force miners to produce valid blocks; the reward and punishment incentivize them to do so. All the protocol needs to do is ensure that only valid blocks with Proof of Work are accepted.
 
 The fairness protocol pattern can also be found in many different aspects of the Lightning Network: