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wtf last won the day on February 7

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  1. I looked back at your comments in this thread and perhaps I missed your question, can you please repeat it? The only question I saw was that you asked what is the additive inverse of a + bi; and it's of course -a =bi. If there was another question I did not see it.
  2. ps -- I don't think my previous explanations were very good. I found a much better page explaining this matter. If you google "why can't you distinguish i from -i" you get hundreds of totally irrelevant hits no matter how you alter or rephrase the question. Took me a while to find this. https://math.stackexchange.com/questions/177594/how-to-tell-i-from-i/177601#177601 The right answer is that there's an automorphism of [math]C[/math] that takes [math]i[/math] to [math]-i[/math]; namely, complex conjugation. In other words the difference between the two amounts to a relabeling with no
  3. -a -ib. Why are you asking such an elementary question whose answer you perfectly well know? If z is a complex number, -z is its reflection through the origin. Perhaps you'll find this helpful. There are no positive or negative complex numbers because it's not possible to put a total order on the complex numbers that is compatible with their addition and multiplication. https://math.stackexchange.com/questions/788164/positive-and-negative-complex-numbers Or https://en.wikipedia.org/wiki/Complex_number#Ordering
  4. I'm afraid I didn't see where you said what it is. There are no positive or negative numbers in the complex numbers, that's why you can't unambiguously use the sqrt sign convention that works in the real numbers.
  5. OP never came back? After crossposting this to two different discussion forums?
  6. Yes. The notation [math]\sqrt{-1}[/math] is often used casually, but it's imprecise in the branch of science, profession, or art of mathematics.
  7. Me being the picky type, let me point out that [math]\sqrt{-1}[/math] is not good notation and is technically not correct. In the case of a nonnegative real number [math]x[/math], we can define [math]\sqrt x[/math] as the positive of the two values whose square is [math]x[/math]. However in the complex numbers there is no concept of positive or negative. That is, we can't algebraically distinguish between [math]i[/math] and [math]-i[/math]. So we define [math]i[/math] as a complex number such that [math]i^2 = -1[/math]. We pick one of the two possible values and call it [math]i[/mat
  8. pps -- I looked at your handle and found this. You most definitely do know how to do math markup. Can you please do us a favor and mark up this linear algebra post?
  9. ps -- I follow everything up to this line. If you can please put in proper parens and show exactly how you got this I'd find it very helpful. Also please note that the [math]y_i[/math]'s are presumably taken to be all distinct from each other, else you can't be sure they contain a linearly independent subset. And also note that when ask us to consider the equation you need to specify that at least one of the [math]c_i[/math]'s is not zero. There's no reason they couldn't all be. When you say, "We cannot have all c_i=0 [individually]in an exclusive manner since that would ma
  10. I saw your similar post on another site where it didn't get any traction. May I suggest a couple of minor notational changes that will improve clarity? Since [math]e \in V \setminus W[/math], I'd call it [math]v[/math]. Likewise I'd call the [math]y_i[/math]'s [math]w_i[/math]. These minor changes would decrease the cognitive burden on the reader; and (if you don't mind my saying) your exposition here and on the other site are already a little convoluted and the reader can use all the help they can get. This notation's hard to figure out. You did convince me on the other site that [mat
  11. I don't believe this is true. sqrt(1) = 1 by definition, assuming by Root(1) you mean [math]\sqrt{1}[/math]. The square root of a positive real number is the positive of the two numbers whose square is the number. So if someone asks, find [math]x[/math] such that [math]x^2 = 1[/math], the answer is {1, -1}. But if someone asks what is [math]\sqrt{1}[/math], the answer is 1. There is no solution to the question in the title. What is true is that [math]- \sqrt{1} = -1[/math].
  12. I happened to run across this terrific talk called The Secret Life of Quarks, well worth watching. https://www.youtube.com/watch?v=H_PmmMkGyx0 Like others, I'd always heard there are 3 quarks inside the proton. Turns out it's not really true. 3 is the number of quarks minus the number of antiquarks. But it's not a matter of counting and subtracting. Rather, you integrate something called the quark density function, and when you do, you get the answer of 3. The actual number of quarks and antiquarks depends on the scale at which you look. So there could be millions, zillions, whatever
  13. Thanks for the info. As a suburbanite I'm just getting over the shock of learning that cheeseburgers are made of chopped up dead cows. I had no idea.
  14. The nearest horse is far from where I live. But my point was that horses foal (if you say so); they don't horse. Whereas evidently, lambs lamb. Which I didn't know. Now I'm gonna take it on the lam.
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