Rigorous Foundations of Real Exponents and Exponential Limits скачать в хорошем качестве

Rigorous Foundations of Real Exponents and Exponential Limits

#RealAnalysis #Mathematics #AdvancedMath #ProofBasedMath #SoME4 #Exponentiation #RealExponents #MathLecture #MathematicalProof #RigorousMath #LimitTheorems #SequencesAndLimits #AnalysisCourse #RealPowers #EpsilonDelta #AMathematiciansLecture #calculus #sequences#convergence link to the full playlist:    • Calculus 1: What is a sequence? Rigorous d...   I would also recommend that you check of the best undergraduate level books in Calculus I ever encountered: https://amzn.to/3dDASMj 🔔 Click the bell in order not to miss new videos! If you liked the lecture and the materials, any support on Patreon: https://www.patreon.com/user?u=40016607 PayPal: https://paypal.me/mathphysics3141?loc... or math.physics3141@gmail.com Visit the store to find cool items related to the channel, mathematics, physics and engineering: https://mathphysicsengineering.creato... shopping in the store is a great way to support the channel. Check this coll shirt with the visual proof from the video printed on it. https://mathphysicsengineering.creato... You can be among the very few people in the world that have this unique custom-designed shirt. This is a full, proof-based reconstruction of real exponentiation, developed from first principles using rational approximations. We go far beyond simply defining the exponential function. This lecture establishes, in complete rigor and detail, all key properties of real powers from the ground up. Every step is proven. No shortcuts. No appeals to results without justification. This result is not assumed. It is earned. It is fully proved. This lecture took enormous effort to create — not only in its technical construction, but in its dedication to completeness, precision, and pedagogical clarity. It is part of a broader vision: a course that gives all the proofs, fills in every gap, and treats serious learners with the respect they deserve. What makes this lecture unique: – Complete formal rigor: no hand-waving, no "just trust it" – All exponent rules are derived from the definition via rational sequences – Real analysis at a level of depth rarely seen, even in top university courses – Motivated explanations paired with airtight proofs