- #1
Saracen Rue
- 150
- 10
Does anybody know what the factorial form of a googolplex would be?
Mentallic said:So you're asking to calculate the inverse gamma function, since the gamma function and the factorial are closely related. i.e. you want to solve for n in
[tex]n!=10^{10^{100}}[/tex]
I can give you a quick start on the approximate magnitude of n. Since a crude approximation is [itex]n!\approx n^n[/itex], then choosing [itex]n=10^{100}[/itex] gives us
[tex]n^n=\left(10^{100}\right)^{\left(10^{100}\right)}=10^{100\times 10^{100}}=10^{10^{102}}\approx 10^{10^{100}}[/tex]
hence n is somewhere in the ballpark of a googol.
Unless of course, you meant something else by your OP. Maybe you were asking what [tex]10^{10^{100}}![/tex] is?
A googolplex expressed in factorial form is a mathematical notation that represents the number 10^(10^100) or 10 to the power of a googol, which is a 1 followed by 100 zeros. It is expressed as 10!(10^100) or 10 x 9 x 8 x...x 2 x 1 x (10^100).
A googolplex expressed in factorial form is a much larger number than a regular googolplex. While a regular googolplex is 10^(10^100), a googolplex expressed in factorial form is 10^(10^(10^100)), which is exponentially larger.
A googolplex expressed in factorial form is significant because it is used to demonstrate the concept of infinity and the vastness of numbers. It is also used in theoretical mathematics and physics to represent extremely large quantities.
The notation for a googolplex expressed in factorial form was invented by Edward Kasner, an American mathematician, in the early 20th century. He introduced the concept of a googolplex in his book, "Mathematics and the Imagination," published in 1940.
No, a googolplex expressed in factorial form is too large to be written out in digits. It has more digits than there are atoms in the observable universe. It is often represented using scientific notation, which is 10^(10^(10^100)).