Count Up with the Four Fours Puzzle √4

[emlightened]

This is a reboot of this old game after I found myself wanting to play it, but not wanting to deal with numbers that large.

In this thread, we count up using the classic four fours puzzle: how high can we get with only four fours. You can use standard arithmetic operations, square root, factorial, and any other operation you can think of (so long as it doesn't involve other numbers and you define it), but please try not to use ceiling or floor. We'll see how high we can go.

You can use the same representation as from the other thread, but try not to copy until you're stuck. Make the numbers however you want!

0 = 4⁴ - 4⁴

[patzer]

If non-integers are allowed-

4/(4^(4^4) = approx. 3*10^-154

If not-

(4-4)^(4^4) = 1

[emlightened]

Yeah, we're just doing 0, 1, 2 etc. 4^(-4)^4^(4!) is smaller though

2 = 4/4 + 4/4

[flicky1991]

3 = 4 - (4/4)^4

[emlightened]

4 = 4 * (4-4) + 4

[flicky1991]

5 = 4 + (4/4)^4

[emlightened]

6 = 4 + (4+4)/4

[flicky1991]

7 = 4 + 4 - 4/4

You can use the same representation as from the other thread, but try not to copy until you're stuck.

The reason why I hadn't posted until now. I was officially stuck - I thought of this one independently of the other thread but saw it was there and couldn't think of another.

[emlightened]

8 = (-4) + (-4) + (-4)*(-4)

You can use the same representation as from the other thread, but try not to copy until you're stuck.

The reason why I hadn't posted until now. I was officially stuck - I thought of this one independently of the other thread but saw it was there and couldn't think of another.

Uh. Hmm. Okay, Imma change that rule. It was meant to be a sort of "try to be more creative than copying, but if you get stuck or come up with the same thing, don't worry".

Thanks for saying so! ^^

[flicky1991]

9 = (√4) * (4 + (√4)/4)

First to take advantage of the rules allowing square root.

[emlightened]

10 = √4⁴ - 4 - √4

[Actaeus]

11 = 4!/√4 - 4/4

[flicky1991]

12 = 4!/((4+4)/4)

[emlightened]

13 = (4! + 4/√4) / 4

13 = (4! + 4/√4) / √4

[flicky1991]

13 = (4! + 4/√4) / 4

I assume that final 4 should be √4?

14 = 4 + √4 + 4*√4

[emlightened]

Yep!

15 = √4⁴ - √4/√4

[flicky1991]

16 = √4⁴ - 4 + 4

[username5243]

17 = 4*4+4/4

[thunk]

18=√4*√4*√4/(.\overline{4})