CH02::intro: remove statements that Bitcoin requires trust

Users operating a full node don't need to trust anyone else for certain
guarantees about the system, although they do need at least one honest
peer to obtain some other guarantees.  Clarify this in the text by
revising text about text and emergent properties.

ch02.asciidoc

@@ -6,13 +6,13 @@
 ((("bitcoin", "overview of", id="BCover02")))((("central trusted
 authority")))((("decentralized systems", "bitcoin overview",
 id="DCSover02")))The Bitcoin system, unlike traditional banking and
-payment systems, is based on decentralized trust. Instead of a central
-trusted authority, in Bitcoin, trust is achieved as an emergent property
-from the interactions of different participants in the Bitcoin system.
+payment systems, does not require trust in third parties. Instead of a central
+trusted authority, in Bitcoin, each user can use software running on
+their own computer to verify the correct operation of every
+aspect of the Bitcoin system.
 In this chapter, we will examine bitcoin from a high level by tracking a
-single transaction through the Bitcoin system and watch as it becomes
-"trusted" and accepted by the bitcoin mechanism of distributed consensus
-and is finally recorded on the blockchain, the distributed ledger of all
+single transaction through the Bitcoin system and watch as it
+is recorded on the blockchain, the distributed ledger of all
 transactions. Subsequent chapters will delve into the technology behind
 transactions, the network, and mining.