Being finite is a feature of certain types of cryptocurrency. Some cryptos have finite number (Bitcoin has 21 million), and others have infinite amounts (generated by mining). That feature is defined by the formulas and computer code that describe the Blockchain protocol (the agreement that everyone uses when they interface with the Blockchain).

How can you prove it? Computer Science. You can examine the source code and the formulas for yourself. Then you can compile it to an executable program.

When you run the executable program, it interfaces with the Blockchain protocol and works.

If the software is not right, it won't interface with the Blockchain. Since all the miners use the same software (consensus), someone cannot come along with modified software and change the blockchain, except in a 51% attack.

In the 51% attack scenario, a bad actor (say the CIA or China) throws enough computing power at the Blockchain to provide a majority of the mining computational power. They can then "Double-Spend" and change values in Bitcoin wallets.

The PROBLEM with a 51% attack is that the bad actor is then left with worthless Bitcoins. Why? Because EVERYONE will know when the Blockchain is attacked, and at that point, everyone abandons the Blockchain. The stolen coins become worthless because no one will give money for coins on that Blockchain.