Yes, $0.999\ldots$ (repeating) is equal to 1. This can be shown using a simple algebraic proof:

1. Let $x = 0.999\ldots$.
2. Multiply both sides by 10: $10x = 9.999\ldots$.
3. Subtract the original equation from this result: $10x - x = 9.999\ldots - 0.999\ldots$.
4. Simplifying, you get $9x = 9$.
5. Dividing both sides by 9: $x = 1$.

Thus, $0.999\ldots = 1$.

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Related Questions:

1. What is a repeating decimal, and how is it different from a terminating decimal?
2. How does the concept of limits in calculus relate to $0.999\ldots = 1$?
3. Can other repeating decimals be simplified to a fraction?
4. How does this concept work in different number systems, like binary?
5. What are some real-world applications where repeating decimals are important?

Tip: Understanding why $0.999\ldots = 1$ helps strengthen your grasp of concepts like limits and the real number system.