Asymptote

In mathematics, an asymptote is a value a function approaches more and more closely as some variable runs out to infinity, without ever quite touching it. The curve 1/x is the classic example: as x grows, the value gets arbitrarily close to zero but never lands there.

Bitcoin has two famous asymptotes baked into its monetary policy.

The supply asymptote. Bitcoin's total supply is the sum of every block subsidy ever paid out. The subsidy started at 50 BTC per block, and gets cut in half every 210,000 blocks (a halving). The geometric series sums in the limit to exactly 21,000,000 BTC. But in practice the subsidy is paid in satoshis (the integer unit; 10^-8 BTC), and each halving divides it by 2 with integer truncation. After 33 halvings, the per-block subsidy rounds to zero satoshis and stays there forever. The total ever issued at that moment is 20,999,999.9769 BTC - just shy of the round number. That's Bitcoin's true supply asymptote. The "21 million" you'll see quoted everywhere is a marketing-friendly rounding of it.

The inflation-rate asymptote. Bitcoin's annual rate of new issuance (the subsidy × blocks-per-year / circulating supply) is currently about 0.83%. Each halving cuts it roughly in half. After the 2028 halving, it drops to ~0.4%. After 2032, ~0.2%. The function approaches zero, reaching its sub-satoshi equivalent around the year 2140. From that point forward, no new BTC enters circulation; miners earn only transaction fees. Bitcoin becomes the first major monetary asset in history with a mathematically-fixed zero-inflation steady state.

Both asymptotes were chosen deliberately by Satoshi Nakamoto. They aren't artifacts of careless code; they're the monetary-policy commitment baked into the protocol. No central authority can change them without forking the network, and the economic incentives against doing so are overwhelming - the value of Bitcoin to its holders comes precisely from the fact that these curves are fixed and verifiable.

The asymptote is what makes Bitcoin a fixed-supply asset in the mathematical sense, not just the rhetorical one. See Disinflation for the rate trend in detail and the Supply Schedule rabbit hole for the full math.