floor(0.999...)=?

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.

Transcript

okay that's to sum up for fun here we're going to do the floor of 0.99 infinite amount of nice first of all we have to know that this right here represents a limit the limit of the sequence starting 0.9 and then 0.99 and then 0.99 and so on we need to find out the limit of that sequence first and be careful this right here represents a limit inside... Read More

Key Insights

• ⛔ The limit of the sequence 0.9, 0.99, 0.999, and so on is 1.
• 🤣 The floor function is used to find the limit, and in this case, it does not change the value of 1.
• 🤝 The order of the limit and function matters when dealing with a discontinuous function.
• 🤣 The floor function of an integer value is equal to the integer itself.
• 🤣 The floor function rounds down to the nearest integer.
• 🤣 The sequence with a finite number of nines after the decimal point, when applied to the floor function, results in 0.

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.