The Biggest Number

This topic has intrigued mathmeticians for centuries. What’s the biggest number? Well, technically there is no biggest number, cuz u just keep doing +1, but let’s look at the limits if I use 270=> chars! (More about chars in the java post)

Addition

Don’t get me started.

Multiplication

As far as I’m concerned, 9*9*9… 135 9’s (because you need 1 char for the *) is 9^135 but we could just use 5 chars-9^135.-

Exponentiation

This is where things become intriguing. 9^9 is essentially 9 multiplied by itself 9 times: 9*9*9*9*9*9*9*9*9. If I applied this to 270 characters, it would result in 9^9^9... which is already extremely large! But hold on...

Tetration and Bases

Tetration is basically repeated exponentiation. Like 3^3 is 3*3*3, 3^^3 is 3^3^3! If we did 9^^9 67 times, then added 1 factorial, that would be unimaginably large, but we are looking for more. Much more. Bases allow you to change the value of each digit in a number. We normally use base 10, where the digit to the left is 10 times more than the other. But if we used base 16, we have each digit being worth 16 times the other ones! Base 16 also introduces digits A, B, C, D, E, and F, each worth one more than the other, continuing throughout the alphabet. So what if we had ZZZZZZ in base 9999? We would get Z*9999^2+Z*9999+Z. Z is 35 in base 10. So what would we get if we had ZZZZZZZ…135 times in base 9999999…135 times? Even though it is very big, I think we can do more! Let's keep going! :)

Note: Repeated factorials donut work because you need parentheses like(9!)! Becase 9!! Is just 2*4*6*8

A Grander Form of Tetration

But wait. Why should we stop there? You could roast me in a million ways by answering my question, but anyway, let’s continue. If tetration is repeated exponentiation, which is repeated multiplication, why can’t we have repeated tetration? We can have pentation! Pentation is repeated tetration. And if we have repeated pentation, we create hextation! And so on and….

But there is a point to it. It is one simple thing, g0. g0 is 3^^^^3, or 3 hextated to 3. But we can now create g1, which is 3^^^^^^^^^^^3 with the symbol repeated g0 times! I call it g0ation. And we now do 3 g1tated to 3, giving us g2! And so on will give us the most famous g, g64, which is Graham’s number, the biggest answer to a math problem! But now, we can keep increasing g until we get g65, g6^6, g7^^7, gZZZZZ in base 999999999, but now we get g(g(g(g(g(……9)! We have 134 g’s and we factorial it at the end, and we will put that as our biggest number for now! Over and out.