For what value of n is |n-1|+1 equal to 0

First redefine the function:

(n-1) + 1 ... when n-1 ≥ 0 ... n ≥ 1

- (n-1) + 1 ... when n-1 < 0 ... n < 1

then solve it:

n-1+1 = n = 0 (doesn't belong to the interval)

-n+1+1 = - n + 2 = 0, n = 2 (doesn't belong to the interval either)

no solution for n ∈ R