Thanks so much for watching and if you love math proofs at all levels, don't forget to check out *my proofs playlist* for some surprises and cool tricks that you can share with friends/family as well as help elevate you to higher levels of math thinking! ruclips.net/p/PL0NPansZqR_ZSBMSajUBJkvi-OKpl-StS&si=Ti2mGwVGcWFgPufQ 🎁 My mission is to *change lives* through *infinite elite free accessible math education* across all levels and topics, so no matter what high school or college someone attends, or life circumstances someone has, they can reach the *highest mathematical levels* (which is a huge boost in literally everything in life, because math supports critical and logical thinking). If you want to constantly be notified of new math content and/or support my mission, please like ✅, subscribe 🥇 and share ⏩ with everyone who you think can benefit! 🥳 It's free content - why not? 😅
what I love about videos like these is I can learn from it easier as I can just rewatch a certain part if I didn't fully get it please keep doing this, thanks
Hi @ElectriteRoblox thanks so much for your really kind and supportive comment, and positive feedback! 😊 I am so happy you are loving these videos and learning from them, that means a lot to me! 😊 Yes, I've got lots of videos planned for the future on a wide range of topics and I'm very excited to have you as a viewer! 🥳 I hope you have an amazing day/evening/night! 😊
Hi @WolfgangFeist thanks so much for your comment as always! 😊 Yes, that's true, and an important observation! I could have also emphasized this before the Lemma when stating f(1/2)^2 = a because at that point we already knew this (and then the Lemma is for the most general value of the function). As you say, it is a very important special case of the Lemma. It's interesting since it's not possible to define a^x for all x if a is negative (but still possible for fractional exponents x = p/q in lowest terms, where q is an odd number). Thanks so much for supplementing the video with this observation, and I hope you have an amazing day/evening/night! 😊
Hi @RiteshArora-s9x thanks so much for your comment! 😊 I think it's a fundamental statement that likely appears in several books (at least as an exercise) but I don't know of a specific book off the top of my head. I hope you have an amazing day/evening/night! 😊
Thanks so much for watching and if you love math proofs at all levels, don't forget to check out *my proofs playlist* for some surprises and cool tricks that you can share with friends/family as well as help elevate you to higher levels of math thinking! ruclips.net/p/PL0NPansZqR_ZSBMSajUBJkvi-OKpl-StS&si=Ti2mGwVGcWFgPufQ 🎁 My mission is to *change lives* through *infinite elite free accessible math education* across all levels and topics, so no matter what high school or college someone attends, or life circumstances someone has, they can reach the *highest mathematical levels* (which is a huge boost in literally everything in life, because math supports critical and logical thinking). If you want to constantly be notified of new math content and/or support my mission, please like ✅, subscribe 🥇 and share ⏩ with everyone who you think can benefit! 🥳 It's free content - why not? 😅
Excellent
It is mind blowing explanation
what I love about videos like these is I can learn from it easier as I can just rewatch a certain part if I didn't fully get it
please keep doing this, thanks
Hi @ElectriteRoblox thanks so much for your really kind and supportive comment, and positive feedback! 😊 I am so happy you are loving these videos and learning from them, that means a lot to me! 😊 Yes, I've got lots of videos planned for the future on a wide range of topics and I'm very excited to have you as a viewer! 🥳 I hope you have an amazing day/evening/night! 😊
I really loved the way you took us through the research process
At 6:01 we might emphasize in addition, that this also shows that a will always be >= 0.
Hi @WolfgangFeist thanks so much for your comment as always! 😊 Yes, that's true, and an important observation! I could have also emphasized this before the Lemma when stating f(1/2)^2 = a because at that point we already knew this (and then the Lemma is for the most general value of the function). As you say, it is a very important special case of the Lemma. It's interesting since it's not possible to define a^x for all x if a is negative (but still possible for fractional exponents x = p/q in lowest terms, where q is an odd number). Thanks so much for supplementing the video with this observation, and I hope you have an amazing day/evening/night! 😊
Sir which book is question from ? Thanks
Hi @RiteshArora-s9x thanks so much for your comment! 😊 I think it's a fundamental statement that likely appears in several books (at least as an exercise) but I don't know of a specific book off the top of my head. I hope you have an amazing day/evening/night! 😊