Integers are just all the positive and negative (and zero) whole numbers. Anything that you can write without a decimal point is an integer.
The rational numbers are defined as any number you can make by dividing one integer by another. (Except for dividing by zero). They are things that can be written as a ratio, like 1/2 is rational, 420/69 is rational.
Irrational numbers are all those numbers that *cannot* be written that way. We know what some of them are because they have special properties, but the vast majority of them are completely unknown because we don’t have a good way of writing them. But examples include pi, sqrt(2), and the number e.
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