floor(0.999...)=?  Summary and Q&A
TL;DR
The limit of the sequence 0.9, 0.99, 0.999, and so on is 1, and the floor function of 1 is also 1.
Questions & Answers
Q: What does the sequence 0.9, 0.99, 0.999 and so on converge to?
The sequence converges to the limit of 1. This can be found by taking the limit of the sequence as n approaches infinity.
Q: Is the floor function involved in finding the limit of the sequence?
Yes, the floor function is used to find the limit of the sequence. The floor function is applied to the limit, resulting in the value of 1.
Q: Why is it important to consider the order of the limit and the function when dealing with a discontinuous function?
The order of the limit and the function matters because a discontinuous function can behave differently depending on the order. In this case, the limit is taken first, and then the floor function is applied.
Q: What is the output when the floor function is applied to the value 1?
When the floor function is applied to the value 1, the output is also 1. The floor function rounds down to the nearest integer, and since 1 is already an integer, it remains unchanged.
Summary & Key Takeaways

The content discusses finding the limit of a sequence that starts with 0.9 and adds infinite nines.

The limit is found by taking the floor function and the limit, resulting in the value of 1.

The floor function of 1 is also 1.