Transcription
What is the absolute largest number you can create using only three nines? Most people would start simple. They'd say 999.
A clever student might multiply them together. But 9 * 9 * 9 is actually 729. So, our number got smaller.
To get a truly massive number, we have to move up the ladder of mathematical operations to exponents. Multiplication is just repeated addition, but exponents are repeated multiplication. We could write 99 to the power of 9. That means 99 multiplied by itself nine times. It gives you a number that's 18 digits long.
But what if we flipped it? 9 to the power of 99. Now we're taking the number 9 and multiplying by itself 99 times. That's a 95-digit long number. That's more digits than there are atoms in the universe. But a math major will tell you that number is still way too small.
What you can use is a power tower. 9 to the power of 9 to the power of 9. We calculate this from the top down. We look at the top two nines. 9 to the power of 9 equals 387 million, which means our tiny three-digit tower becomes 9 to the power of 387 million. How big is that number? It has exactly 369 million digits. If you wrote down 10 digits every single second, it would take you over a year of nonstop 24/7 writing just to write the number down.
But even the math major is wrong. If multiplication is repeated addition and exponents are repeated multiplication, then what is repeated exponentiation? It is a terrifying concept called tetration. Instead of putting the exponent on the top right, you write it on the top left. 99 tetrated to base 9. It's a 9 to the power of 9 to the power of 9 repeating 99 times.
So, if a three-level power tower takes a year to write out, then what would a 99-level power tower do? The number of digits in this number is so large that if you turned every atom in the universe into a hard drive, you would run out of space before you even wrote the first fraction of a percent of this number. And you just did it with three nines.