I have heard that [...] when more miners join, the value of bitcoins would rise because there would be additional resources that would be used to process the transactions.

I do not see why more validation power would make the currency unit more valuable. But before this discussion, lets clarify the technical side.

In general, the idea behind the Bitcoin protocol is to achieve a consensus view on the common transaction ledger in a decentralised way, i.e. no third-party intermediary to act as a clearing agency etc. To avoid double-spending of coins, transactions need to be verified by miners before insertion into the blockchain - also, all nodes will synchronise with the longest chain available, so effectively the system works on a majority-based consensus system (majority of the miners determine the global chain).

Now, this would open up to security problems - one example is the Sybil attack, where an adversary simply creates countless virtual identities who all vote for his (potentially false) chain.

This is where the Proof-of-Work (PoW) scheme used in Bitcoin's mining protocol comes in. It is purposefully made computationally difficult for miners to verify blocks. Because of this, miners need to invest resources (energy, money) in order to participate - the rationale is that it is much harder to fake computational power in the network than simple identities, preventing a Sybil attack.

Back to the value of Bitcoin: Note that the following is rather subjective, and highly controversial.

I argue that it is simply determined by market supply and demand. Following this basic logic, the value of 1 BTC must increase in the number of users to join the network, since the monetary base of Bitcoin is limited by design. Because this is unrealistic in the long run, this argument can not be final.

On top of this, we can see extreme levels of speculation on cryptocurrency exchanges, driven by developments such as

• adaptation (e.g. recognising Bitcoin as legal tender in some countries, more vendors' acceptance...)
• news flow on upcoming updates, increasing awareness of cryptocurrencies and the resulting interest by the public and corporations
• negative economic/political activity in some economies might lead to more demand for bitcoin

On the contrary, miners enter or leave the mining process based on whether the potential reward for successfully mining a block is "worth" the work, with the value of the reward being strictly based off the current market value of a bitcoin.

Yes, this is correct. A causality between hashing power and the market value of 1 BTC is not apparent, other than that new miners will likely participate in the system themselves, increasing demand. Rather, as the market value increases, mining becomes more attractive in the short run. Note that after each 2,016 blocks, mining difficulty is adjusted to maintain a fixed mining rate, so then it becomes more expensive and miners will have to decide if they continue participating.

You are correct as to what influences the price of bitcoin, but the significance of mining and Proof of Work and why it costs time/ energy and money is due to fact that the number of valid blocks produced needs to be limited over a period of time and to ensure that it is difficult to rewrite the blockchain.

If it was easy to produce blocks, the network would be flooded with blocks and various chains. It would be very difficult to agree which blockchain is authoritative. Further, if it were not for the difficulty of producing a new block, it would cost nothing to rewrite the blockchain and produce an alternative view of the history of transactions.