*why should* ∣*x*−1∣<*δ hold true*.

The expression \( |x - 1| < \delta \) is typically used in the context of the **epsilon-delta definition of a limit** in calculus. To understand why this inequality should hold true, let's break it down step by step:

1. **Delta (\(\delta\)) represents a small positive number:**  
   In the epsilon-delta definition of limits, we are given an \(\epsilon\) (a small positive number representing how close we want \(f(x)\) to be to the limit), and we need to

Explore why the inequality |x−1| < δ holds true in the context of the epsilon-delta definition of limits. This calculus problem breaks down the core concepts of limits and provides a detailed explanation for advanced students in Grades 11-12.

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