the fact, again (with a definition of e)  Summary and Q&A
TL;DR
The video discusses the fact limit and the definition of the number "e", providing algebraic explanations and examples.
Questions & Answers
Q: What does the video call the limit (1 + alpha/x)^x as x approaches infinity?
The video calls it the fact limit, as it is a significant limit that will frequently appear in calculus.
Q: What is the definition of the number "e" presented in the video?
The video defines "e" as the limit of (1 + 1/T)^T as T approaches infinity.
Q: How is the fact limit related to the definition of "e"?
The video shows that the fact limit and the definition of "e" are equivalent by making a substitution and rearranging the algebraic expressions.
Q: Can the fact be used to evaluate other limits?
Yes, the video provides an example where the fact is used to evaluate the limit of (1  1/2x)^4x as x approaches infinity.
Summary & Key Takeaways

The video introduces the fact limit for the expression (1 + alpha/x)^x as x approaches infinity, calling it the fact.

The definition of the number "e" is also explored, using a limit expression (1 + 1/T)^T as T approaches infinity.

By making a substitution and algebraic manipulations, the fact limit and the definition of "e" are shown to be equivalent.

Examples are given to demonstrate how to use the fact to evaluate limits.