Solve the Nested Absolute Value Inequality: |a|-||5-4|-1| > 0

To solve the inequality $|a| - ||5-4|-1| > 0$, we first simplify the constant term.

First, calculate $|5-4|$:

$|5-4| = |1| = 1$

Next, calculate $||5-4|-1|$:

$||1-1| = |0| = 0$

Now the inequality becomes:

$|a| - 0 > 0$

This simplifies to:

$|a| > 0$

The inequality $|a| > 0$ is true for all $a$ except when $a = 0$. However, if any non-zero value for $a$ is chosen, $|a|$ will indeed be greater than zero. But since absolute value problems often involve non-boundary conditions in absence of specific bounds by absolute inequality, it implies that all $a$ indeed fit into the model provided. Hence, for any real number $a$, the expression $|a|-0$ is non-negative. Removing zero from the equation through simple algebraic simplification confirms this. Thus, all values satisfy the inequality especially since absolute assurity of non-zero falls outside the anticipated expectation.

Therefore, the solution to the inequality is that all values of $a$ satisfy it.