User blog:IAmAPersson/Phillip's Number

Phillip's Number is defined as /text{C(C( 9 →9→ 99 9, 9 →9→ 99 9 ) → 9 → 99 9 → 9 → 99  9  → 9 C( 9 →9→ 99 9, 9 →99))}. I created this number and decided to name it after myself (I didn't really know a good name for it). This is how I obtained this number.

The following text is quoted from my website found here.

My goal for this number was to come up with the largest number I could, while abiding by the following rules:



     Number had to be less than 50 characters (excluding spaces).

''     Only the 5 following notations were allowed:  Up-Arrow Notation, Chained Arrow Notation, Hurford's Extended Chained Arrows, Fonster's Extended Chained Arrows, and Hurford's C Function. ''

    Number had to be made from scratch within a 10-minute time period.

    No infinity (obviously)



My number went through the following steps:



     3 →33

 3 →33 → 33

 3 →3 → 43 3

 9 →9 → 99 9

     C(C(C(9 →9→ 99 9,  9 →9→ 99 9,  9 →9→ 99 9)))

     C( 9 →9→ 99 9, 9 →99)  ↑ 9 → 9→ 99 9  C( 9 →9→ 99 9,  9 →99)

     C( 9 →9→ 99 9,  9 →9→ 99 9 )  ↑ 9 → 9→ 99 9  C( 9 →9→ 99 9,  9 →9→ 99 9 )

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;">     C( 9 →9→ 99 9,  9 →9→ 99 9 )  →9 → 99  3 →9 → 99    C( 9 →9→ 99 9,  9 →9→ 99 9 )

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;">     C(C( 9 →9→ 99 9,  9 →9→ 99 9 )  →9 → 99  3 →9 → 99    C( 9 →9→ 99 9,  9 →9→ 99 9 ))

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;">     C(C( 9 →9→ 99 9,  9 →9→ 99 9 )  →9 → 99  3 →9 → 99    C( 9 →9→ 99 9,  9 →99 ))  → 93

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;">

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;"> Before arriving at my final number:

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;">

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;">       C(C( 9 →9→ 99 9,  9 →9→ 99 9 )  → 9 → 99  9 → 9 → 99   9   → 9  C( 9 →9→ 99 9,  9 →99 )) 

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;">

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;"> I hit 50 characters exactly. I'm pretty happy, because with the knowledge I had about googology at the time of doing this (16), I didn't know how to get much higher with the established ruleset. I did decide to not use Up-Arrow or Hurford's Chained Arrows in my final number, as I knew that Fonster's Chained Arrow notation was much more powerful than either of those. I used the C function to use only 3 characters, but to make the number skyrocket. I know that C can take 3 arguments, but I didn't have the space for that in the direction I was going. I also used all 9s because, well, it's the highest 1-digit number.

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;">

<p style="color:rgb(0,0,0);font-family:Oxygen,sans-serif;line-height:19.5px;"> So, in conclusion, the only goal for this number was to be  ridiculously  huge. I know that I could have made larger numbers by using functions like TREE, but that felt like cheating to me, so I didn't allow that function when establishing my rules. I'm pretty happy with my result. This number has no significant value whatsoever; it was made for fun (however, rules were still in place, so I was under restriction!) If we started to simplify my number using standard rules of C and Chained Arrows, we'd get something like this: <span style="color:rgb(58,58,58);font-family:Helvetica,Arial,sans-serif;">/text{ C(C( 9 →9→ 99 9,  9 →9→ 99 9 )  → 9 → 99  9 → 9 → 99   9   → 9  C( 9 →9→ 99 9,  9 →99 ))} <span style="color:rgb(58,58,58);font-family:Helvetica,Arial,sans-serif;">/text{ C( 9 →9→ 99 9,  9 →9→ 99 9 )  → 9 → 99  9 → 9 → 99   9   → 9  C( 9 →9→ 99 9,  9 →99 )   → C( 9 →9→ 99 9,  9 →9→ 99 9 )  → 9 → 99  9 → 9 → 99   9   → 9  C( 9 →9→ 99 9,  9 →99 ) C( 9 →9→ 99 9,  9 →9→ 99 9 )  → 9 → 99   9 → 9 → 99   9   → 9  C( 9 →9→ 99 9,  9 →99 )} <span style="color:rgb(58,58,58);font-family:Helvetica,Arial,sans-serif;">/text{ (( 9 →9→ 99 9)  →C(9→9→ 99 9,9→<sup style="line-height:20.8px;">9→99 9-1 ) ( 9 →9→ 99 9))   → <sup style="line-height:20.8px;"> 9 →99   9 → <sup style="line-height:20.8px;"> 9 →99   9   → 9 (( 9 →9→ 99 9)  →C(9→9→ 99 9,9→<sup style="line-height:20.8px;">9→99 9-1 )  ( 9 →9→ 99 9))   → <sub style="line-height:20.8px;"> C( 9 →9→ 99 9,  9 →9→ 99 9 )  → 9 → 99   9 → 9 → 99   9   → 9  C( 9 →9→ 99 9,  9 →99 )    (( 9 →9→ 99 9)  →C(9→9→ 99 9,9→<sup style="line-height:20.8px;">9→99 9-1 )  ( 9 →9→ 99 9))   → <sup style="line-height:20.8px;"> 9 →99   9 → <sup style="line-height:20.8px;"> 9 →99   9   → 9 (( 9 →9→ 99 9)  →C(9→9→ 99 9,9→<sup style="line-height:20.8px;">9 9-1 )  ( 9 →9→ 99 9))} As you can see, this number is getting  massive. All I've been doing is just 3 levels of sorting out the C functions. The visual size of this number in extended chained arrows is...well...I'll let you guess how large that is. And guess what? Now simplify it to where the number is in standard chained arrow notation. Yea...huge. Now guess what? Evaluate that chain. This number is big.