BlogHide Resteemsshinday (30)in mathematics • 4 years ago[Apostol's Calculus] Exercises 1.5: Solution to 25Let S be the set of all vectors v such that v = < x , y, z > with 3x + 4y = 1 and z = 0. Then, x = and y = So, v = Proof: Assume S is a real linear space, then S must be…shinday (30)in mathematics • 4 years ago[Apostol's Calculus] Exercises 1.5: Solution to 23Let S be the set of all vectors v = in V3 with either x = 0 or y = 0. Assume S is a real linear space. Then, S must be closed under addition (axiom 1). Let v1 = ∈ S and let v2 = ∈ S…shinday (30)in hive-124500 • 4 years agoCompilation of Solutions to Tom Apostol's Infamously Rigourous Calculus Textbook (vol. 2)Hello! Someone else has already compiled solutions to all exercises in Tom Apostol's "Calculus", but on for vol. 1. As I am taking multivariable calculus this semester, I've decided it would be…shinday (30)in mathematics • 4 years ago[Apostol's Calculus] Exercises 1.5: Solution to 14Let S be the set of all functions f such that Assume that S is a real linear space. Then, by the addition axioms of real linear spaces, there must exist an element g in S such that f + g = 0. We…shinday (30)in mathematics • 4 years ago[Apostol's Calculus] Exercises 1.5: Solution to 11Let S be the set of all functions ƒ such that for all x in their domain, the function is increasing. In other words, S = { ƒ | ƒ' > 0 ∀ƒ } Assume that S is a real linear space. Then S will be…shinday (30)in mathematics • 4 years ago[Apostol's Calculus] Exercises 1.5: Solution to 5Let S be the set of all functions f such that f (1) = 1 + f (0). Assume that S is a real linear space. Then S must be closed under addition. In other words, if g(x) is in S, then the…shinday (30)in apostol-calculus • 4 years ago[Apostol's Calculus] Exercises 1.5Notice: These proofs are my own. I am not a professional mathematician. If you notice errors or inconsistencies in these solutions, let me know! I appreciate all feedback. The key to solving these…shinday (30)in mathematics • 4 years agosteemCreated with Sketch.Tom Apostol's "Calculus" vol. 2; My Solutions to ExercisesPlease note this is a work in progress. I will update this page (with links) as I gather more solutions. This is an ongoing project that I expect will take close to a year to finish. Links:…shinday (30)in philosophy • 7 years agoThe Presocratics Part 1 — "Introduction"This is a part of my series on the Presocratics, the Greek philosophers who flourished before and during the life of Socrates. This is an ongoing series detailing their ideas and importance in a…shinday (30)in writing • 7 years agoThe Feynman Technique (Studying Not More, But Stronger)As is the case with all skills, learning is something that takes practice and gradual improvement to do par excellence. There are several things you can do to improve your learning (To name a few:…shinday (30)in philosophy • 7 years agoPhilosophy Series on the Pre-Socratics!Hello! I have been reading a lot on the history of Greek philosophy. I have become very interested in this topic due to some existential angst I've been having. Personally, I have found studying…shinday (30)in philosophy • 7 years agoOn The Multiverse: The "Nackiverse" Thought ExperimentI feel like everything is conscious. When I say everything, it is crucial to understand what that entails. To "exist" is the sole parameter for being. All things within our universe exist. Every…
