Children of morta gif4/19/2023 ![]() Then you discover this formula: "How many ways are there to choose k things out of n things?" It turns out to be (n!)/((k!)((n-k)!)). We're not sure it makes any sense, but, ok. So if 0! were to equal SOMETHING, it should probably be 0!=1!/1=1. How do we get from one to the next one? You might see that 3! = 4!/4. If we look at the sequence of factorials: 4!=24, 3!=6, 2!=2, 1!. So if you're going to have an abstraction like this, you have to make sure it is internally consistent with math overall, and then see how that abstraction applies to reality. Quantum physics looks totally bananas, with imaginary numbers everywhere-except then it describes how particles actually behave. So imaginary numbers are an abstraction, but they model real world things. Well, it turns out that, by using imaginary numbers, you can figure out what the "real" answer is (in both senses of the word "real"). They knew there was a real, actual answer (it is big when x is big, and very negative when x is negative, so there had to be an answer somewhere in the middle). Are you familiar with imaginary numbers? They feel like nonsense-in what world could have a number, i, and then you make a square of length "i", and that square has area -1? Nonsense, right?Īt some point people were trying to figure out how to solve cubic equations, things like x 3 - 3x - 7=0. However, sometimes that abstraction allows us to find out about things in the real world. So, you're right: math is an abstraction of the real world.
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