In mathematics, there is no limit to the size of numbers that can be expressed. As long as you have enough digits, you can keep counting up to larger and larger numbers. However, when it comes to practical applications, there are some limits to the size of numbers that we can use or even imagine.
In the context of modern computing, the largest number that can be represented by a 64-bit system is 2^64 – 1, or approximately 18.4 quintillion. This is because a 64-bit system uses 64 bits, or binary digits, to represent a number, and each bit can either be a 0 or a 1. With 64 bits, there are 2^64 possible combinations, or approximately 18.4 quintillion.
However, there are mathematical concepts and theories that allow us to talk about much larger numbers, even if we cannot represent them with a finite number of digits. For example, in set theory, there is a concept called the “power set” of a set, which is the set of all possible subsets of the original set. The power set of a set with n elements has 2^n elements. This means that even a relatively small set can have an unimaginably large number of possible subsets.
In addition, there are some mathematical notations that allow us to represent extremely large numbers compactly. For example, the number googol is a 1 followed by 100 zeroes. The number googolplex is even larger, and is represented as 10^googol, or a 1 followed by a googol of zeroes. These numbers are so large that they are difficult to comprehend, and have few practical applications beyond their use in mathematics and theoretical physics.
In conclusion, there is no one “biggest number” in the world, as the concept of a number is abstract and infinite. However, in practical terms, the largest number that can be represented by a 64-bit system is approximately 18.4 quintillion, and there are mathematical concepts and notations that allow us to talk about much larger numbers.