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There is no such thing. As soon as you find the "largest number" you could just add one and it would be bigger. Again and again forever.
That symbol is used for a number, which is approximately 2.718. It is one of the most important numbers in mathematics, together with pi - both appear over and over again, in many places. The number "e" is the base of the natural logarithms.
When you raise a number to a power, you multiply it by itself. If you multiply any number by 1, it does not change. So, when you raise 1 to a power, you just multiply 1 by 1 over and over again. This also applies to negative powers, where you are simply dividing 1 by 1 repeatedly.
A fraction is written with one number (the numerator) on top of another number (the denominator) with a horizontal line separating them; the number on top is being divided by the number on the bottom. That's what fractions mean. One divided by two is one over two which is one half.
A recursive rule is one which can be applied over and over again to its own output