BLOCKCHAIN & WEB3 FUNDAMENTALS - Chapter 5, Exercise 2 Solution
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Why Halving Caps Total Supply at 21 Million

PROBLEM
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Using this chapter's own halving schedule (50 BTC starting reward,
halving every 210,000 blocks), explain in your own words why Bitcoin's
total supply approaches but never exceeds 21 million, rather than
continuing to grow forever.

SOLUTION
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New bitcoins are only ever created as the block reward paid to
whoever mines each block, and that reward keeps getting cut in half
every 210,000 blocks. Each successive halving period therefore adds a
smaller total amount of new bitcoin to the supply than the period
before it, even though each period covers the same number of blocks.

Roughly:
- Blocks 1 to 210,000: reward is 50 BTC/block, adding up to about
  10.5 million BTC total over this period
- Blocks 210,001 to 420,000: reward is 25 BTC/block, adding about 5.25
  million BTC
- Blocks 420,001 to 630,000: reward is 12.5 BTC/block, adding about
  2.625 million BTC
- ...and so on, each period adding roughly half as much new supply as
  the period before it

This is exactly the same shape as adding 1/2 + 1/4 + 1/8 + 1/16 and so
on forever - a sequence where each new term is smaller, and the
running total gets closer and closer to a fixed ceiling without ever
actually reaching or crossing it. Eventually the reward, expressed in
the smallest unit Bitcoin can represent, rounds down to zero rather
than continuing indefinitely as an ever-smaller fraction, which is
what stops the process rather than it continuing mathematically
forever - and it's this halving-and-eventually-rounding-to-zero
process, expected to finish around the year 2140, that produces the
real, fixed 21 million total.

ANSWER: Because each halving cuts the new-coin issuance rate in half
rather than resetting it, each successive four-year period adds
roughly half as many new bitcoins as the period before it - a
shrinking, converging sequence that adds up to a fixed total (21
million) rather than growing without bound, ending once the reward
eventually rounds down to zero.

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WHY THIS WORKS AS AN ANSWER

This explains the actual mathematical shape of the halving schedule
(a converging, halving-each-period sequence) rather than just
restating "the supply is capped," making clear why that specific
mechanism produces a fixed ceiling instead of unbounded growth.