Is a googol the same as infinity?

Question

10^100 is a googol. Some sources say this is infinity. I though infinity couldn't be quantified? What's up with that? And what does this guy mean? "A googolplex is precisely as far from infinity as is the number one." — Carl Sagan, Cosmos

Answer 1

Nope, googol has a finite value. It's a big number but by no means anywhere close to the concept of infinity.



In fact, the number "googolplex" is bigger than googol. It's the same as 10^(googol). You can imagine googolplexplex = 10^(googolplex), googolplexplexplex, etc. Each of those would still not be close to infinity. There would still be infinitely many more numbers to count before you got to infinity.



As for Carl Sagan's statement. Since infinity is the concept of something immeasurable, you can actually subtract finite values from ∞ and you still have ∞.



Thus, you could subtract 1, or you could subtract googol, or you could subtract googolplex, etc. and you still wouldn't have reduced the distance to infinity. Infinity is unreachable so it really doesn't matter how far you have gone, you'll never get there. The remaining distance is still ∞.

Answer 2

Infinity is not a real number. Infinity is what you said. It is just a concept to help prove problems in higher maths including, perhaps most notably, projective geometry and of course Calculus.



a googol is a real number and is exactly as you put it. a 1 followed by 100 zeros or 10^100.



The 2 are most definitely not the same.



A googolplex is still a real number but is much larger than googol. A googolplex is 10^googol. In other words 10^10^100.

It is basically an impractical number and I suppose you could get away with saying it is as far from 1 as infinity but it is incorrect to say that it is "precisely" as far as infinity.



A googolplex is still a real number. It is proven that given any real number, there is a real number still larger than your starting number.

By definition, there is no number larger than infinity.



Thus, googolplex and infinity are not the same thing.

Answer 3

No. Infinity is not a number.



He means that there are as many numbers in between 1 and infinity as there are between a googolplex and infinity because infinity doesn't have a limit.

Answer 4

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 is a google it is far away from infinity. for the same reason that .99 repeating is the same as 1.

Answer 5

It has to deal with limits. When you raise 10 to the 100th power, the rate at which the function is increasing when you approach 100 is so large, it is nearly the same.

Answer 6

you are absolutely right, you cannot assign a value to infinity