If we choose to have a tail emission in our money after the initial emission curve, it means that technically the amount of coins is going to be infinite. With every new block new coins are born, so if we keep creating blocks we’ll keep creating coins as well, those new coins are added to the already existing quantity of coins in circulation, therefore dilluting the value of each coin.
Here’s where the tail emission being a fixed amount comes in handy. Let’s say our initial emission is 100 coins, and then we add a constant tail emission of 1 coin per block. The moment that new coin is out, it instantly made the other 100 worth a little less, because now there are 101 coins to purchase the same amount of stuff. We could say that roughly, it’s worth 1% less. But what happens if we keep doing it? Well, it’ll keep happening and our money will keep diminishing in value. At which rate though? At less than 1%. When we create the second new coin, there are 102, then 103, and so on. But if we calculate the percentages, they’ll be 0.9%, 0.8%, 0.7%… What’s going on? What’s happening is that every new coin is a smaller part of the big pile of existing coins. That means that with every new coin the entire set of coins loses a tiny bit less value than before.
That’s called asymptotic. It’s a term for a number that gets closer and closer but never totally reaches a certain value. In this case, the inflation percentage gets smaller and smaller yet never gets to zero. Is it still technically infinite? Yes. But so do coastlines for that matter.