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The biggest well-defined finite number is not a specific number, but rather it depends on the system of mathematics being used. In the standard system of decimal (base-10) notation, the largest finite number is 9,999,999... with an infinite number of 9's, which is commonly referred to as "nine nines" or "googol."

However, in other systems of mathematics, such as binary (base-2) or hexadecimal (base-16), the largest finite number is different. For example, in binary notation, the largest finite number with n digits is 2^n - 1. In hexadecimal notation, the largest finite number with n digits is 16^n - 1.

It is also important to note that there are infinite sets of numbers that are not finite, such as Irrational Numbers and infinity itself.

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