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www.jeremykun.com | ||
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mathscholar.org
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| | | | | [AI summary] The text presents a detailed, self-contained proof of the Fundamental Theorem of Calculus (FTC) using basic principles of calculus and real analysis. It breaks the proof into two parts: Part 1 establishes that the integral of a continuous function defines a differentiable function whose derivative is the original function, and Part 2 shows that the definite integral of a continuous function can be computed as the difference of an antiderivative evaluated at the endpoints. The proof relies on lemmas about continuity, differentiability, and the properties of integrals, avoiding advanced techniques. The text is structured to provide a clear, step-by-step derivation of the FTC for readers familiar with calculus fundamentals. | |
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jeremykun.wordpress.com
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| | | | | Last time we investigated the (very unintuitive) concept of a topological space as a set of "points" endowed with a description of which subsets are open. Now in order to actually arrive at a discussion of interesting and useful topological spaces, we need to be able to take simple topological spaces and build them up... | |
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0fps.net
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| | | | | In this post, I am going to go into a bit of a mathematical digression about the fundamentals of solid modeling. In a nutshell, solid modeling is the study of digital representations of physical shapes. This was a hot topic in the early days of computing and computer aided design, and led to some pretty... | |
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qualiacomputing.com
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| | | [AI summary] The text discusses a framework for understanding subjective time as a causal network of local binding connections. It explores how different states of consciousness, such as those induced by psychedelics, can alter this network, leading to various experiences of time, including time loops, moments of eternity, and timelessness. The framework also connects these experiences to emotional valence and the structure of consciousness, suggesting that symmetry and regularity in the network contribute to positive emotional states. The text concludes by emphasizing the potential of this approach as a starting point for further research into time perception and consciousness. | ||
