From "a*x^2+b*x+c = 0" follows "x1 = (-b + sqrt(b^2-4*a*c))/2*a"
indicating that the second part is the only solution.
Strictly speaken, since no equivalence has been used, this even means that there is either no solution, or if there is a solution, it must have the form "x1 = (-b + sqrt(b^2-4ac))/2*a".
However, I'm willing to admit that this is nitpicking.
> indicating that the second part is the only solution.
I'm not familiar with a notation in which implication means "only". As in:
x = 4 -> x > 3
does not in any way imply that x is the only number larger than 3, or that x is only larger than 3. I specifically wrote "x1" to indicate _a_ solution, not _the_ solution; if it was _the_ solution, there would have been no need for the "1" index.
> it must have the form "x1 = (-b + sqrt(b^2-4ac))/2*a".
Alternatively, since sqrt could be the multi valued function with no specific branch selected, this actually does give all the solutions.
> However, I'm willing to admit that this is nitpicking.
And I can't even find any appreciation for it - Because you picked a set of assumptions (x is Real or Complex, sqrt is a specific branch of a multi-branch function, no natural order for solutions) treated as axioms, but question others, where said axioms actually determine correctness.
Are you sure I was not, in fact, describing an equation in Z_2?
Nitpicking at this level, especially if you do it often, might make you feel good about yourself, but doesn't actually get you anywhere.
-- beagle3, who started professional life as a mathematician and switched to engineering at a later stage.
I'm afraid this is a misunderstanding. What I was trying to say is that if the right-hand side of an implication denotes a single solution, there can't be any other solution.
For instance, if you write something like this:
x^2 = 4 -> x = 2
this means that all solutions to "x^2 = 4" must satisfy "x = 2", which means that there can't be more than one solution. Any other solution than "2" would be a counter-example to this implication.
And since there is another solution, namely "x = -2", the implication above is wrong. In other words, from "x^2 = 4" is does not necessarily follow that "x = 2".
However, I agree that writing "x1" instead of "x" (as you did) kind of solves this notational issue.
> Alternatively, since sqrt could be the multi valued function with no specific branch selected, this actually does give all the solutions. [...] Are you sure I was not, in fact, describing an equation in Z_2?
Of course, nitpicking never stops.
If sqrt() was meant to be a multi-values function, why did the formula denote "x1"? Also, was "^" ment to be "power" or "bitwise XOR"? Is "sqrt" a product of four variables? And so on.
That is the whole point about admitting "nitpicking": We agree in how the formula is to be interpreted, so there is no need to get deep into formalities, as long as the real issues behind the whole stuff are clear (which they pretty much are).
> Nitpicking at this level, especially if you do it often, might make you feel good about yourself, but doesn't actually get you anywhere.
Correct me if I'm wrong, but this seems to be a mere ad hominem, not an actual argument. It is also a straw man, because I never claimed that this kind of nitpicking leads to somewhere. In my previous comment I was even implying quite the opposite.
> Correct me if I'm wrong, but this seems to be a mere ad hominem, not an actual argument. It is also a straw man, because I never claimed that this kind of nitpicking leads to somewhere. In my previous comment I was even implying quite the opposite.
You are wrong, but I will not correct you, as my sarcasm detector beeps strongly here. Correct me if I'm wrong.
HN supports unicode characters. You could have simply copied it from somewhere else, e.g. the Wikipedia (http://en.wikipedia.org/wiki/Plus-minus_sign):
±
However, simply writing "+/-" would also have been good enough for this purpose. Ugly formulas are preferable to wrong formulas.