1^inf approach 1 vs I^inf doesn't approach 1

Do math for fun with brilliant.org, https://brilliant.org/blackpenredpen/ , first 200 people to sign up will get 20% off your subscription, and you can support my channel too! brilliant#4, 1^inf approach 1 vs I^inf doesn't approach 1, In this video, I explain the common misconception of 1^inf, and the limit of a product vs. product of the limits. Hope you guys like it and find it helpful. My previous video on n!/n^n, which is technically wrong, https://www.youtube.com/watch?v=ZsvGl-9f8rI , The corrected version of n!/n^n, will be here soon. The fact, by L'H', https://www.youtube.com/watch?v=HM-kwHR4VO4 , The fact, by def. of e and algebra, https://www.youtube.com/watch?v=2nUJMP_ZnnI&t=26s , blackpenredpen math for fun, brilliant.org/blackpenredpen, tags, limit of n^3/(n+1)^3, limit of n^n/(n+1)^n, 1/e, An example that 1^inf does NOT approach 1