> is there any practical constraints or applications around it? To speak to this question: Suppose you were going to build a calculator program on your compute

> is there any practical constraints or applications around it? To speak to this question: Suppose you were going to build a calculator program on your computer. You might start with integers and have addition multiplication and subtraction. All perfectly fine. Even if the numbers are very big you can still represent them by using multiple memory slots. The you add division, and since you don’t want rounding errors in your calculator, you add rational numbers. Can rational numbers still be represented by a computer? Yes, because they are a countable infinity, you can represent them just as easily as you can represent integers. You would like your calculator to be as complete as possible so you keep adding functions like roots, exp, log, sin, et cetera. But no matter how many functions you add, you’ll never be able to represent every real number. This is useful to know so that nobody ever tries to build a computer that does this.