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Am currently a physics student who is doing research using a mathsy. An approach to solve a physical system might be. Your cup of tea as it is maths applied directly to an application but still keeps. The savviness of big old derivations that you are probably more thinking of. A mathematician Official Pharm Tech Crushing It Shirt lines like Spivak does. That’s just to make the exposition completely clear. A mathematician would do exactly what you did, but instead of saying “divide both sides by a”, he would say, “multiply both sides by a-inverse”. The reason for this is, the mathematician doesn’t think there are two things, multiplication, and division. That takes too much work to remember. Multiplication is complicated enough to worry about, so you use them. Properties of multiplication to talk about “division”. Math is the supreme art of laziness. “How do you get the most ideas out of the fewest thoughts? Ok. So happy.

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You missed the point of the example exercise you gave. Just like you don’t prove the Pythagorean theorem each time you need it, you don’t write 5 lines each time you want to divide both sides of an equation. The point of the exercise is to explain why (and when. You can divide Official Pharm Tech Crushing It Shirt. The point of the exercise is to tell that division is nothing more than multiplication by the inverse. The point of the exercise is also to teach you rigor. But rigor does not mean always building everything from the ground up. It means bridging your starting point to your endpoint without leaving any gap. In particular, everything can be built from the ground up, and that’s beautiful. But you only need to do it once. Here, you should have understood. And that’s a fairly low starting point, at least for non-logician.

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