Say Alice buys 1 BTC and Bob 100 BTC. Nakamoto defined coin(BTC) as a "chain of digital signatures", so Alice bought 1 such chain, and Bob 100 chains. That makes no sense to me, so could you please explain?
1 Answers
The Bitcoin system enables its participants to collaboratively maintain a ledger of balances, the Unspent Transaction Output (UTXO) set. Satoshi referred to what we today call “UTXOs” as “coins” in his writing. The rules of the system ensure that new funds are only created per a limited reward for extending the blockchain. Hence, the amount of bitcoin tracked in the shared ledger is strictly capped and predictable. Due to the system's global reach, reliability, scarcity, utility, and transparency, bitcoin represents a verifiable record used among bitcoiners as payment for goods and services or repayment of debt.
UTXOs are uniquely identifiable and hold a discrete amount of bitcoin. To transfer funds, a sender submits a transaction to the network which can be understood as an announcement declaring some specific UTXOs to be expended and some new UTXOs to be issued. The sender proves ownership of the claimed UTXOs by providing cryptographic signatures satisfying the spending conditions encoded in each of the UTXO when they were created.
Since each UTXO results from a pedigree of preceding transactions, it could be poetically described as stemming from “a chain of digital signatures”.
If you are looking for a more philosophical treatise of what Bitcoin is, you may find Craig Warmke's “What is bitcoin? [PDF]” interesting. He's a Professor of Philosophy at Northern Illinois University and provides a metaphysical model for how to think about Bitcoin in the linked ~43 page work.

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So, what does it mean when Alice bought 1 "Unspent Transaction Output" and when Bob bought 100 "Unspent Transaction Outputs"? I don't get it? Where is that 100 times bigger amount of "Unspent Transaction Outputs" keep for Bob and what Bob can do with that property? – niwrad Aug 25 '22 at 15:46
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1@niwrad think UTXOs has physical coins and bills, with different denominations. For example, Alice has $1, in one bill of $1. Bob has $100, but it could be 1 $100 bill, or 2 $50 bills or 10 $10 bills, etc. Bills = UTXOs, UTXOs != BTC. What we call now UTXO it was Satoshi called Coin. – bordalix Aug 26 '22 at 05:33
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The transaction output specifies the amount of bitcoin that is assigned to the receiver. It can be any amount from 0 to all bitcoins. However, a sender cannot assign more to a receiver than they spent. – Murch Aug 26 '22 at 11:59
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@bordalix Having $100 bill means owning 100 debt units created in the US banking system. $=debt/loans. So, a dollar bill is just a way to tell people that they own debt. Likewise, bitcoin wallet tells Bob to own 100 BTC, that is coins. Checking the definition of a coin, we see "chain of digital signatures". That chain is recorded on blockchain. So, it follows that the wallet tells Bob to own 100 units of blockchain. And the blockchain is only one. And it is free for everyone to download. Now this has even less sense. – niwrad Aug 28 '22 at 07:41
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@Murch So you're saying that UTXO is coin, and coin is UTXO? – niwrad Aug 28 '22 at 07:47
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Yes, "coin" was the word Satoshi used for "UTXO". – Murch Aug 28 '22 at 10:56
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1@niwrad maybe my analogy with bills is not the best one. Maybe it would be better to imagine UTXOs as bank checks, because UTXOs can have any denomination. For example, Bob owns 100 BTC, by having one UTXO of 42.42 BTC and another of 57.58. When Bob pays 1.23 BTC to Alice, he uses the 42.42 UTXO to generate a UTXO of 1.23 BTC for Alice, and a new UTXO of 41.19 for himself (his change). He can also aggregate UTXOS, i.e. send his UTXOs to himself to get one single UTXO with the total. The sum of all UTXOs is equal to the available BTC (~19 millions) – bordalix Aug 29 '22 at 05:55
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@bordalix So analogically, having one wallet with 42.42 USD in it, and another one with 57.58 USD, means having 100 USD. Ok, that's just a way how information about ownership of USD is organized. In the same way someone can have one TSLA stock certificate with 100 written on it, and another with 500. But this doesn't define USD or TSLA. USD is debt created in the US banking system. TSLA is equity of Tesla company. Debt or equity is what people transact with. What's the thing that people transact with in the bitcoin system? What is BTC? – niwrad Aug 29 '22 at 14:55
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Bitcoin is backed by the full faith of the people that accept Bitcoin. It's exactly these entries in the UTXO set and nothing more. Turns out that some people want to have more of them and offer to trade other currencies, goods, or services for that. – Murch Aug 31 '22 at 12:00
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Perhaps check out: https://bitcoin.stackexchange.com/q/182/5406 – Murch Aug 31 '22 at 12:02
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@Murch The question here is what is BTC? If Alice has 1 BTC, and Bob 100 BTC written in their wallets, the system informs Bob that he owns a hundred times more of something than Alice. What is that something? If we replace BTC with TSLA, USD or XAU, the brokerage or bank systems inform Bob that he owns a hundred times more equity units, debt units or metal units than Alice. So what exactly is that thing behind the name BTC? Satoshi defined it as chain of digital signatures. That's nonsensical, because that chain is stored on blockchain and thus freely available to anyone. Bob doesn't own it. – niwrad Aug 31 '22 at 16:02
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It's a set of ledger entries maintained by the collective bitcoin network. Pretty much the same as your bank statement might have a bigger or smaller number than someone else's bank statement or how you might have two beers on your tab at a bar while another patron only has one beer on the tab. The main difference being that there are more people enforcing the shared rules and contributing to writing updates to the ledger. – Murch Aug 31 '22 at 16:07
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In other words, it's an abstract thing like many other forms of money. – Murch Aug 31 '22 at 17:54
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My bank statement informs me how how many debt units I own. The same as brokerage statement informs me how many equity units/shares I own. The chain of entries stored on blockchain is not something that Bob owns. Blockchain is a public ledger own by no particular person or organization. So it seems that Bob owns nothing. Just as I thought. – niwrad Sep 01 '22 at 09:34
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While Bob doesn't own the chain by himself (but co-owns it with all other participants), nobody but Bob can spend his units accounted in it, because spending his coins requires a signature from his private key. – Murch Sep 01 '22 at 12:26