Count to the biggest number

[shant93]

RULES & INFO
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I believe this is a yearly math competition at MIT, I may or may not be mistaken. Anyways, I am starting one here, and I may or may not be the first. Anyways, the goal is to write a number, or a mathematical expression, whose value is greater than the one of the previous post. Do not grow too quickly or you will ruin the fun. If possible, post wikipedia links of the operators you are using to help people understand.
Furthermore, to keep this fun, I am imposing a 10-character limit. I will start with one and try to introduce new operators every time.
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BEGINNING
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1

[lemon-tree]

Root 2
√2

[shant93]

3 factorial
3!

3 x 2 x 1

[lemon-tree]

How could you skip Pi?
Anyway, log2 128

[shant93]

2^^3

(2^2)^2

[lemon-tree]

|10+(√101)i|

= 18.52

[shant93]

(e^e)+e+e

= 20.59

Isn't i the square root of -1? so wouldn't √i be even more imaginary?

Also, we should probably wait for new users to post.

[alexandgruntz]

Root i is 0.707+0.707i. (1 over root 2 plus 1 over root 2 i)

Expression: 10Pi :D

[lemon-tree]

I added in brackets to make it more obvious what I meant.
pi^(29/9)

[shant93]

ln(20!)

log in base <e> of 20!

=42.34