Is it permissible for the value to be exactly 0, or must it be strictly greater than or less than 0? 

In the context of limits, it is perfectly permissible for the value of a limit to be exactly 0. The limit of a function as \( x \) approaches a certain point can indeed be 0 if the function's value approaches 0 as \( x \) gets closer to that point.

In the problem you provided:

\[
\lim_{{x \to 0}} \frac{x}{{20 - x}} = 0
\]

The result being 0 is valid and means that as \( x \) gets closer to 0, the value of the function \( \frac{x}{{20 - x}} \) approaches 0. There's no requirement for the limit to be strictly greater than or less than 0; the limit can indeed be exactly 0, as it is in this case.

Would you like to explore situations where limits might be strictly greater than or less than 0?

### Related Questions:
1. What conditions would cause a limit to be positive or negative infinity instead of 0?
2. How does the concept of approaching a value differ between finite limits and limits at infinity?
3. Can you have a limit that does not exist, and if so, under what circumstances?
4. What is the significance of a limit being exactly 0 in real-world applications?
5. How do you interpret one-sided limits where the limit might approach 0 from above or below?

### Tip:
When calculating limits, pay attention to whether the function could approach 0 or another specific value from different directions (left or right) to determine if one-sided limits might give more insight.

Explore the concept of limits in mathematics and understand when it is permissible for a limit to be exactly 0. Detailed explanation with an example of \( \lim_{{x \to 0}} \frac{x}{{20 - x}} = 0 \) provided.

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