user243: Just to check what would take for that limit to be changed. (not that I want to be changed, quite the opposite). I know the total number of bitcoin reward is halved every 4 years.
So does the verifying nodes check if the number of rewarded bitcoins match the distribution schedule?

user479: The software in the bitcoin client verifies that each transaction follows the algorithm that is part of the protocol.
Now even if the developers of the client were to somehow conclude that increasing the limit was a good idea and were to then push that client out for distribution, those holding bitcoins would likely not accept the new client.  There would then be a fork in the blockchain as the limit increase would devalue the currency already issued and therefore it would be rational to those holding bitcoins already would protect the value of their currency by not accepting transactions from the new fork.
So to change the limit you not only need to get the developers to make the changes that fork the blockchain but also you need to get exchanges and merchants to accept transactions using the fork -- something that, in this case, is irrational.

user9128: An updated answer.
First, check out the block subsidy calculation: https://github.com/bitcoin/bitcoin/blob/v23.0/src/validation.cpp#L1417
CAmount GetBlockSubsidy(int nHeight, const Consensus::Params& consensusParams)
{
    int halvings = nHeight / consensusParams.nSubsidyHalvingInterval;
    // Force block reward to zero when right shift is undefined.
    if (halvings >= 64)
        return 0;

    CAmount nSubsidy = 50 * COIN;
    // Subsidy is cut in half every 210,000 blocks which will occur approximately every 4 years.
    nSubsidy >>= halvings;
    return nSubsidy;
}

An important constant: consensus.nSubsidyHalvingInterval = 210000 comes from this file here:
https://github.com/bitcoin/bitcoin/blob/v23.0/src/chainparams.cpp#L67
Right now the current block height is 704673 (you can look it up here if you like: https://blockexplorer.one/bitcoin/mainnet)
halvings = int(704673 / 210000) == 3
So the current reward 50 >> 3 == 6.25
The sum of a series that halves like that is a/(1-r), where a is the first value (50) and r is the ratio (0.5). See: https://en.wikipedia.org/wiki/Geometric_series for more info.
Thus 50 + 25 + 12.5 + 6.25 + 3.125 + 1.5625 + … + 0.000000001 = 100
Since the same amount is given per block, you need only multiply that by the total number of blocks issued per halving:  210000
210,000 * 100 == 21,000,000
Bitcoin is an open source consensus protocol.  It's not a company, there is no "foundation", and the code can be reviewed by anyone with about a high school level of knowledge of math.

user323: Every node in the Bitcoin network checks every block it receives and validates any transactions in it. As coin generation is a transaction that is included in the block, it is also checked. Same as a node would not accept a transaction that does not balance its inputs and outputs (for example, by spending more coins than it has), neither would it accept a block reward different, than the one that is scheduled to occur (50 coins currently, half of that for some number of blocks, and then other fractions of that amount). The nodes know what rewards to expect based on the block number, as it is set to half based on that number.
To change it you would have to (convince people to) change all the clients, exactly like any other protocol change.

243: <p>Just to check what would take for that limit to be changed. (not that I want to be changed, quite the opposite). I know the total number of bitcoin reward is halved every 4 years.</p>

<p>So does the verifying nodes check if the number of rewarded bitcoins match the distribution schedule?</p>
 479: <p>The software in the bitcoin client verifies that each transaction follows the algorithm that is part of the protocol.</p>

<p>Now even if the developers of the client were to somehow conclude that increasing the limit was a good idea and were to then push that client out for distribution, those holding bitcoins would likely not accept the new client.  There would then be a fork in the blockchain as the limit increase would devalue the currency already issued and therefore it would be rational to those holding bitcoins already would protect the value of their currency by not accepting transactions from the new fork.</p>

<p>So to change the limit you not only need to get the developers to make the changes that fork the blockchain but also you need to get exchanges and merchants to accept transactions using the fork -- something that, in this case, is irrational.</p>
 9128: <p>An updated answer.</p>
<p>First, check out the block subsidy calculation: <a href="https://github.com/bitcoin/bitcoin/blob/v23.0/src/validation.cpp#L1417" rel="nofollow noreferrer">https://github.com/bitcoin/bitcoin/blob/v23.0/src/validation.cpp#L1417</a></p>
<pre><code>CAmount GetBlockSubsidy(int nHeight, const Consensus::Params&amp; consensusParams)
{
    int halvings = nHeight / consensusParams.nSubsidyHalvingInterval;
    // Force block reward to zero when right shift is undefined.
    if (halvings &gt;= 64)
        return 0;

    CAmount nSubsidy = 50 * COIN;
    // Subsidy is cut in half every 210,000 blocks which will occur approximately every 4 years.
    nSubsidy &gt;&gt;= halvings;
    return nSubsidy;
}
</code></pre>
<p>An important constant: <code>consensus.nSubsidyHalvingInterval = 210000</code> comes from this file here:
<a href="https://github.com/bitcoin/bitcoin/blob/v23.0/src/chainparams.cpp#L67" rel="nofollow noreferrer">https://github.com/bitcoin/bitcoin/blob/v23.0/src/chainparams.cpp#L67</a></p>
<p>Right now the current block height is 704673 (you can look it up here if you like: <a href="https://blockexplorer.one/bitcoin/mainnet" rel="nofollow noreferrer">https://blockexplorer.one/bitcoin/mainnet</a>)</p>
<p><code>halvings = int(704673 / 210000) == 3</code></p>
<p>So the current reward <code>50 &gt;&gt; 3 == 6.25</code></p>
<p>The sum of a series that halves like that is <code>a/(1-r)</code>, where a is the first value (50) and r is the ratio (0.5). See: <a href="https://en.wikipedia.org/wiki/Geometric_series" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Geometric_series</a> for more info.</p>
<p>Thus <code>50 + 25 + 12.5 + 6.25 + 3.125 + 1.5625 + … + 0.000000001 = 100</code></p>
<p>Since the same amount is given per block, you need only multiply that by the total number of blocks issued per halving:  210000</p>
<p><code>210,000 * 100 == 21,000,000</code></p>
<p>Bitcoin is an open source consensus protocol.  It's not a company, there is no &quot;foundation&quot;, and the code can be reviewed by anyone with about a high school level of knowledge of math.</p>
 323: <p>Every node in the Bitcoin network checks every block it receives and validates any transactions in it. As coin generation is a transaction that is included in the block, it is also checked. Same as a node would not accept a transaction that does not balance its inputs and outputs (for example, by spending more coins than it has), neither would it accept a block reward different, than the one that is scheduled to occur (50 coins currently, half of that for some number of blocks, and then other fractions of that amount). The nodes know what rewards to expect based on the block number, as it is set to half based on that number.</p>

<p>To change it you would have to (convince people to) change all the clients, exactly like any other protocol change.</p>
