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There is no largest number. One simple way to consider this is to look at the function:
f(x) = x + 1
Pick any number, and plug it into that function. No matter what number you plug in, the function will always give you a number that is one larger than the previous one. It doesn't matter how big "x" is, there will always be an "x + 1" value, which will always be larger than x. This is a concept we refer to as infinity, which is usually represented with the symbol ∞. It is important to note that infinity is not in itself a number, but the concept of a set of numbers that has no limit.
There is however a large finite named number. That would be a googolplexian, which is a one followed by a googolplex of zeroes. A googolplex itself is a one followed by a googol of zeroes, and a googol is a one followed by a hundred zeroes. In other words:
1 googol = 1 × 10100
1 googolplex = 1 × 10googol or 1 x 10^(10^100)
1 googolplexian = 1 × 10googolplex or 1 x 10^(10^(10^100))
There are also large numbers that can only be expressed as complex exponentials, such as Graham's Number. Once again though, none of these are the largest number that exists, as there is no such thing. You need merely to add another value on top to reach a larger number.
999,999,999,999
Most people will say that the largest number on earth is a googol (10100), often misspelt as Google due to the search engine, however a googolplex is bigger than this (10(10)^100 or 10googol) and Graham's number is even greater still (and is the biggest number to my knowledge)
The is no practical "highest" number as you can always add "and one more" to a number. In mathematics infinity (sometimes symbolically represented by ∞) is regarded as the number at which there is no higher number. This may be thought to be the number you get when you divide 1 by 0 (∞=1/0)
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