One of the most common questions I get when interfacing with regulators, financial executives, or anyone else relatively new to Bitcoin revolves around the 21,000,000 BTC issuance limit.

The Bitcoin protocol specifies that only 21 million BTC will ever be minted for all time by the miners who support the network. Transaction fees will ideally take over after the minting is done, which theoretically could sustain the network at that point, but my focus is on questions around whether a hard coded limit of currency issued makes the long term feasibility of BItcoin questionable.

I get the sense from central bank types that fixed issuance is a non starter for them and I’m hoping to mitigate some of those concerns with this analysis. The natural questions that arise:

1) Why 21 million?

2) Doesn’t this limit the supply or hamper the distribution to people?

…and more. I’m only focusing on #2 for the purposes of this blog post. #1 is slightly interesting but not that interesting.

Every time I get this question, it’s hard not to have my thoughts drift back to my undergrad days, when I learned about real numbers, the famous mathematician Georg Cantor and critically, the cardinality of the continuum.

Right now, 1 BTC can be divided into 1 / 100,000,000 of a coin, commonly known as a Satoshi. In practice we can have arbitrary precision for this sort of thing in the event that BTC becomes so valuable that even a smaller fraction than that would be worth a significant amount. So let’s idealize BTC as being represented as a real number. This is a critical point.

One of the most unintuitive aspects of real numbers is that they are a special type of huge. When we think of infinity, there are actually many classes of infinities, some larger than others. Natural numbers (1, 2, 3, …) are one type of infinity but it turns out real numbers, such as 3.14159… represent a much larger type of infinity. Cantor called the “size” of real numbers the cardinality of the continuum.

It’s tempting to think that the interval (-infinity, + infinity) is much larger than (0,1) but in the real number line (or the continuum), this is not the case. They are both the same size in a very tangible sense.

If we can always map one member of a set to another, one to one, then this is a useful definition of comparable size. The classic example is the tangent function. There is a one to one mapping between the function y = tan(x) where x is an element of (-pi/2, pi/2) and y ranges from (-infinity, +infinity). So in a precise sense they are the same size, despite one interval looking much, much smaller than the other.

The consequence is counterintuitively startling — if no fundamental lower bound quantum (such as a USD penny) is specified, and a digital currency has precision along the reals, then the total number of BTC issued is completely irrelevant. Whether 1 BTC, or 1 billion BTC is issued for all time, the abilities of the currency remain the same.

So don’t fret about the 21M BTC limit. It’s real, and it’s all good.

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