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Okay, picking up from the last step, it's cool how they're building this up. The idea of an 'infinitesimally small number' sounds wild, but it's clearly the key to unlocking these advanced math concepts. I'm intrigued to see how it applies to functions and tangents, that's the next logical step.

Whoa, switching gears to calculating curved areas already! That definitely sounds like a much harder problem than just finding a slope. I can see why they'd say it's impossible with a standard number system. This is where the infinitesimal numbers really need to shine.

Ah, so the strategy is to break the area down into super thin rectangles. That makes sense, conceptually. Each rectangle is tiny, almost like an infinitesimal width itself. This is starting to feel like a visual puzzle they're solving with numbers.

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The speaker introduces the third step in understanding calculus, building upon the concepts of infinitesimally small numbers and their application to finding the slope of a tangent line on a curve [0:00]. This initial segment establishes the foundational building blocks, highlighting the power of infinitesimals to overcome limitations in traditional number systems. The focus quickly shifts to a new problem: calculating the area under a curved function [0:30].

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