I think I ran into my limit of replying to replies on this thread, but I would like to add @sigmajin that yes I am still defending that solutions to infinite series are not nonsense. We all learn math like we learn science. You probably learned that atoms were the smallest thing, maybe then you learned that those were made up of smaller things, then possibly you learned about quarks and the rest of the known subatomic particles. Did you tell your science teacher that they were wrong because you previously learned that atoms were the smallest thing? Or did you accept that maybe you were given the best way to understand what you needed at the time you were learning it and now you were going a little deeper in the way the world works? The same with infinite series. How could you pass calculus without being at least a little humbled by what you think makes sense and what the numbers show don't always line up? You're basically adding an infinite number of rectangles with zero width when you integrate, but you get the right answer. Fractional reserve banking means that banks can loan out more money than deposits they take in. When the economy grows, then the bankers are happy. When people spend money, it has a positive effect on the economy. But, when people (or businesses or governments) are unable to pay their bills because they don't have enough savings and there isn't enough new money coming in, then you have a collapse. People and businesses may file for bankruptcy. Governments may try to print their way out of it, but it ultimately can make the damage much worse. Pretend I'm a bank. I loan money to my friends. I only loan the amount of money that I have in savings. I charge them 10% interest on my loans. I can only get back my $100 plus the $10 interest. Say I'm a fractional reserve Bank. I have $100. I can loan $1,000 to my friends because I can have IOU's. Money comes in different forms. There is not nearly the amount of paper (or coins) that there is in debt and 1's and 0's in the economy. Some wouldn't even call the dollar money anymore because it isn't backed by a physical commodity like gold, silver, oil, etc. It's fiat currency because the US government says that it has value.