Find the value of the following expression:

$$\left| \, |{ -|{-1 + 1}| - 1 }| + 1\right|.$$
We calculate as follows: $$|\,|{-|{-1+1}|-1}|+1| = \left|\, |0-1|+1\right| = |1+1| = \boxed{2}$$
2
Level 2
Algebra
Problem: Find the value of the following expression:

$$\left| \, |{ -|{-1 + 1}| - 1 }| + 1\right|.$$
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve the expression, we start with the innermost part: -1 + 1. This simplifies to 0. Next, we take the absolute value of 0, which is |0| = 0. 

Now we substitute this back into the expression: -|0| - 1. Since |0| = 0, this simplifies to -0 - 1, which is -1. 

Next, we take the absolute value of -1: |-1| = 1. 

Now we add 1 to this result: 1 + 1 = 2. 

Finally, we take the absolute value of 2, which is |2| = 2. 

Thus, the final answer is 2.<|END_OF_LATENT|> The final answer is $2$.