This page grows. Every time a real question comes up, the answer gets added right here, in the same plain words as the lessons. Newest at the top.
Yes. The slices stack up. Every piece you buy lands in your wallet and joins what you already have. Buy enough of them and they add up to a full 1.00000000 Bitcoin. And you do not have to stop there: you can keep going past one whole coin.
Your wallet does not keep the pieces as separate little coins. It just shows one total number that grows every time you buy. So you do not "collect" a specific coin: you grow your balance until it crosses 1 whole coin.
People even have a nickname for doing this slowly: stacking sats (buying a few satoshis, those tiny pieces from the last question, a little at a time). A small buy every week quietly stacks up.
How a miner actually works. The computer is not "solving math" the way you do homework. It is guessing a number over and over, trillions of times a second, until it hits one that counts as the winner. It is basically a lottery where buying more computing power is like buying more tickets. Whoever wins announces it, everybody else double-checks it in a second, and that page of payments becomes final.
Why make them guess at all? All that guessing burns real electricity, which costs real money. That cost is the whole point: to cheat the notebook you would have to out-guess the entire world, which would cost a fortune. So being honest is cheaper than lying. It also keeps new pages coming at a steady pace, about one every ten minutes.
Where the money comes from (two parts):
The brand-new batch gets cut in half every four years or so (called a "halving"). Eventually it reaches zero, and from then on miners are paid by fees alone. That shrinking batch is exactly what makes sure no more than 21 million ever exist.
Rigs, farms, and pools (the things you were asking about):
The fixed number is WHY it has value. Regular dollars slowly lose value because the government can print more whenever it wants, so each dollar buys a little less over time. Bitcoin is the opposite: nobody can ever make coin number 21,000,001. The supply is locked forever.
People wanting it sets the price. Since no new coins can be squeezed in, the price is just a giant auction that never closes: more people trying to buy than sell pushes the price up, and more people trying to sell than buy pushes it down. That tug-of-war happens live all day, the same way a stock price moves.
That is also why the price jumps around a lot (the fancy word is volatile). The locked supply does not make the price steady: it just makes it impossible to water down.
A Bitcoin is not one solid coin. It is a number, and it splits into tiny pieces:
So you never send a whole coin. If a coffee costs $4 and a whole Bitcoin is worth $40,000, you send one ten-thousandth of a coin (about 10,000 sats) and keep the other 99.99 percent.
And you do not do that math yourself. You type "$4" and your wallet figures out the tiny fraction to send. The leftover comes back to you as change, just like a cash register. You walk away with the rest still yours.