Intelligent-Plane555




























  1. personally I think gcd(p, q) = 1 is the superior notation 😤

  2. That is exactly what it means, it’s an operator that negates the term it’s applied to either by subtracting from zero or multiplying by -1.

  3. Those are two different things. They may both work on a number line, but subtracting a value from zero and multiplying it by negative 1 are fundamentally different. First of all, you’re using a negative number to define negative numbers which doesn’t work. Mathematicians define negative numbers as vein additive inverses of their counterparts. Kind of like antimatter, if you much it with its opposite, you get nothing. 3 + (-3) = 0. Likewise (-8) + (-(-8)) = 0. Even though 3+(-3)=0 and -3=0-3 are logically equivalent, definitions are held sacred to mathematicians as nonargumentative. There is no debate to be had since the definition has been used for centuries. On another note, in other algebras, 3+(-3)=0 and -3=0-3 are NOT equivalent, meaning one could be true and the other not. You don’t see that until a 3rd semester algebra course though lol

  4. I think you mean the antiderivative of sine? The function is show is one whose derivative is equal to sine. (Almost everywhere)

  5. I would’ve subtracted y2 from both sides so that both have differences if perfect squares. Haven’t written it out but I assume it falls out nicely from there

  6. Sure is: photons from the sun are scattered by the molecules and atoms in the atmosphere. Blue light frequencies being the most scattered. The scattered photons meet your eyes and you see blue.

  7. That's correct. And as you can see, it has nothing to do with the physical properties of oxygen

  8. What do you teach? Just out of curiosity, how old are you? I’m a 46 yo retired Civil Engineer.

  9. I teach PS topology and differential topology at a university as a student teacher. But I teach algebra 2 at a local high school, hence my example. My father is a civil engineer and he also loves putting everything in decimal, even if it is wrong haha.

  10. I think you may be forgetting about significant figures. When rounding to 2 significant figures, the square root of 2 is ABSOLUTELY 1.41

  11. Caring for significant figures is a way to round numbers. Rounding numbers inherently produces error. Mathematicians choose not to err and do not round numbers. Our goal is not to build thing but to come to general realizations and be rigorous about it.

  12. Instead of Kreutzer, try doing etudes such as Mazas or Dont Op. 37. Kreutzer May look easy at the start, but it is much more challenging that the two series I mentioned

  13. Could that mean to slide up into the note?

  14. Recall that the cardinality of [0, 1] and [0, inf) are precisely equal. Therefore we can form a bijection between [0, 1] and [0, inf), and thus we can also form a bijection in a similar way between uniform distributions from 0 to 1 and 0 to inf.

  15. A bijection exists, but it wouldn’t preserve uniformity like the other commenter notes. There is no linear bijection between those two sets so you’d need some other kind of distribution for [0,inf)

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