Most consecutive positive integers using two 1s

Question

Using two 1s, try to come up with the most consecutive positive integers.

Allowed operations:

• Addition

• Subtraction

• Multiplication

• Division

• Concatenation

• Square Root

• Radical

• Factorial

• Floor and Ceiling Functions

• Decimal Point

Answer 1

Let's try (feel free to add on or correct, this is community wiki):

$1=1\times1$

$2=1+1$

$3=\left\lfloor\sqrt{11}\right\rfloor$

$4=\left\lceil\sqrt{11}\right\rceil$

$5=\left\lfloor\sqrt{\sqrt{\left(\left\lfloor\sqrt{11}\right\rfloor!\right)!}}\right\rfloor$

$6=\left\lfloor\sqrt{11}\right\rfloor!$

$7=\left\lceil\sqrt{\sqrt{11}!}!\right\rceil$

$8=\left\lfloor\sqrt{\sqrt{\sqrt{11!}}}\right\rfloor$

$9=\left\lfloor\sqrt{11}!\right\rfloor$

$10=\left\lceil\sqrt{11}!\right\rceil$

$11=11$
$12=\left\lceil\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\left\lceil\sqrt{\sqrt{\sqrt{\sqrt{(\left\lceil\sqrt{11}\space\right\rceil!)!}}}}\right\rceil!}}}}}\right\rceil$
$13=\left\lceil\sqrt{\sqrt{\sqrt{\left\lceil\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\left\lceil\sqrt{\sqrt{\sqrt{\sqrt{(\left\lceil\sqrt{11}\space\right\rceil!)!}}}}\right\rceil!}}}}}\right\rceil}}}\right\rceil$

$14=\sqrt{\sqrt{\left\lfloor\sqrt{\sqrt{\left\lceil\sqrt{\sqrt{\sqrt{(1\div(.1))!}}}\right\rceil!}}\right\rfloor!}}$