>>16774367 (OP)
I mean, it's not "wrong." But yeah, you'll piss off most serious mathematicians with that statement.
F(x)=Root(x) is not a function if you include the negative solutions so it's pretty much universally recognized that any expression Root(x^2) is equal to Abs(x) rather than +/-x.
This is pretty much entirely a formality thing though.
>>16774396
Yes, and the only thing that would change if it didn't is you'd have to be more explicit in your ranges whenever you evoke it.
It's a formality designed to make things less of a pain in the ass.
>>16774394
There is a function taking a positive real number to its positive square root, yes. This doesn't mean the negative square root is not a square root.
>>16774401
There are no radicals in the highlighted part.
>>16774418 >There is a function taking a positive real number to its positive square root
yes and that function is called the principle square root or positive square root or square root which is what is being talked about in the wiki. >This doesn't mean the negative square root is not a square root.
it does. a function by definition can't output a tuple of values, meaning whatever you use to get -2 from β4 is principally not the same function as the one that outputs 2 from β4. there is no named elementary function that outputs only the negative square root. i suppose you can invent one yourself and call it "negative square root" or something if you want just don't expect people to know what you're talking about when you mention it.
>>16774432 >what is being talked about in the wiki.
The wiki article is talking about square roots as such, which is a purely algebraic concept that applies to rings without positive and negative elements as well. You seem to vaguely remember from your mathematical education that βx is positive (true) and conclude that all square roots are positive (does not follow and is false anyway).
>>16774392 >you'll piss off most serious mathematicians with that statement.
No you won't; quite the opposite. The statement is correct, and takes into account the more general setting. >>16774436 is the only poster ITT who's not a full-fledged moron.
>>16774446
So we could replace those formulae with simply "+ βx" and it would be just as correct?
Try telling that to an actual mathematician.
The root function including the negative range is only considered within niche applications of complex analysis. Try stick y = βx in a graphing calculator and see what comes up.
>>16774445
Because βx^2 = |x|, so if you're e.g. solving a quadratic like x^2 = 3 you must take both cases of the absolute value function into account. This has no bearing on the quoted wiki page (which is correct).
>>16774460
I don't know how many times I can explain this same thing to you. A number y is a square root of x if y squares to x. That is the definition of a square root. I would rather want you to elaborate what do you think is erroneous with this definition instead of vaguely gesturing about formulas having +/- βx in them.
>>16774367 (OP) >>16774394
the function is called the "principal" square root, though sometimes people omit the principal part, which has lead to this confusion
a "regular" square root is not a function, because two inputs are mapped to the same output
this is against the definition of a function, which needs only one input to be mapped to each output
therefore the "principal square root" was devised as a function which is only the positive solution
>>16774432 >yes and that function is called the principle square root or positive square root or square root which is what is being talked about in the wiki.
It is called the principle square root precisely because there are multiple square roots. That word "principle" is not just there for show. Yes, the word is sometimes left out for simplicity if the distinction is clear from context, but in general there is *the* principle square root of 4 whereas -2 is *a* square root of 4.
>>16774469
You are failing to distinguish between the algebraic property of being a square root of a given number vs. the function sending a positive real number to its positive (aka principal) square root.
>>16774473
The wikipedia article describes the principal square root right there in the first line of the second paragraph. It even talks about the relevance of "the definite article".
>>16774526
Who gives a fuck? A square root of a number x is any number y that if you multiply y it by itself gives you x. You're all a bunch of idiots lol. Probably posting from India.
>>16774384
Brother, the heresy goes even deeper than that.
There are no such things as negative numbers. Just like zero, irrationals, and infinities, they are the work of the DEVIL!
Fortunately we are THE ONE TRUE FINITE FAITH are here to oppose such BLASPHEMY.
God is on our side.
Fine squareroot is DEFINED to be positive root if you use the squareroot symbol, BUT if use the definition that should be for a square root.
Squareroot of X is the number that when multiplied by itself equals X.
The traditional definition is, when you think about it, wrong... what idiot defines a function that eliminates half the actual values.
>>16774879
I always hated this image. >be monkeys >monkey does thing >bad shit happens to everyone for reasons beyond our comprehension >punish monkeys who do thing >bad shit stops >everyone forgets why we don't let anyone do thing
What's the lesson even supposed to be? Because it feels like it has these anti-traditionalist overtones while simultaneously making the argument in favor of upholding tradition even if you don't understand why they were put in place.
>>16774898
No. The image does not describe a crab bucket. Not even remotely.
What's being described is one monkey reaching for short term gain that hurts everyone else for some unknown reason. That's almost the opposite of a crab bucket.
>>16774904
The crab bucket analogy is usually used to describe how niggers in the ghetto will hold down anyone trying to make a meaningful improvement on their lives and escape the ghetto.
That is not what the image is showing.
The image shows one monkey acting on impulse and that behavior results in problems for everybody else.
A better analogy would be how societies always go to shit when gay shit gets normalized. Like I can't tell you exactly why faggots ruin societies, but best keep them in check since there seems to be a correlation.
>>16774907 >describe how niggers in the ghetto will hold down
That's what the image shows. >one monkey acting on impulse
That's what a nigger would see.
>>16774909
What's missing from the crab bucket, and crucial to the image, is that all the other monkeys got punished when one monkey reached for the bundle.
>>16774916
With a whip. Or if you're a girl, maybe a whip and then rape? The part of the experiment you think you're in already happened. Crab bucket niggers are that way because they already are, which is literally the point of the eighth panel of that cartoon.
>>16774423
If there were no issue, it would be annotated The inclusion of -4 is invalid, and is presented only for the sake of demonstration."
Any square root where a negative is a valid output will clearly fucking state that in front of the symbol.
>>16774917
The point of the experiment (if it even happened at all) isn't some genetic trauma bullshit. It's inherited culture.
You seriously think this crab bucket shit dates back to slavery?
>>16774924
My default belief is that no social science experiment happened and that, if it did happen, it's not replicable. To the extent that a crab bucket exists as a social niggerism, yes, it obviously dates back to slavery and to whatever other moon howling orbits slavery.
>>16774923 >Every nonnegative real number x has a unique nonnegative square root, called the principal square root or simply the square root...
Huh. Whouda thunk it's on your stupid ass to communicate clearly.
When speaking of something other than the principle square root, please clarify with the appropriate notation preceding the radix.
>>16774933 >who gives a fuck about >whining about semantics
Somehow, I picked up in High School that "the square root" means "principle." I was not aware that I knew this.
Please explain to the thread how you failed to grasp this fundamental precept of communication. >>16774938
Yes,
>>16774947 >well in my school they taught us that the planet is flat so what do you have to say for yourself?
don't make me suffer the consequences of your low shitty third world education
>>16774950
I'm still waiting for you to figure out what I actually said. >>16774948
You can fuck off with that shit. You know precisely what is going on.
>>16774937
It has zero to do with crabs or "niggers" and not being a "nigger" wont get you out of this one. Unless you're a literal NPC sooner or later you're gonna figure out that the way people in your life act are influenced by past events.
Like my dad is a huge worry wart, and it turns out the reason is his the first child of his great grandparents died from SIDS and then the great grandfather died young so his great grandmother got paranoid about risks to her kids. Then when my dad was a toddler, his dad got Rheumatic Fever and got told by the doctors he had at most 10 years to live (he lived until 90) and that excitement could kill him at any time. This made his wife enforce upon the kids that they must never get into arguments or dad might die.
This kind of shit carries over into later generations as obsolete conditioned behaviors and "family disposition" sometimes "family curse", unless you make a conscious effort to stamp it out.
>>16775148
So you were wrong and 1 can't actually have an arbitrary number of roots, it can only have 1 and -1 as its roots and you can't even name an actual number whose roots are arbitrarily many?
>>16775151 >So you were wrong
Again, you're lacking basic logical literacy here. "Can have" is not the same as "must have". >name an actual number whose roots are arbitrarily many
Take a ring, choose an element and keep adjoining distinct square roots of that element. Adjoin as many as you like.
>>16775157 >Again, you're lacking basic logical literacy here.
No, you said any number can have arbitrarily many roots only to immediately contradict yourself and admit that 1 can not have arbitrarily many square roots since only 1 and -1 work.
>Take a ring >a
So the number 1 since ring is not number? >keep adjoining distinct square roots of that element.
Not possible as there are only 2 distinct square roots of 1, so you can't keep doing it arbitrarily since there are only 2 square roots of 1 rather than arbitrarily many.
>>16775160
1 can have more than two square roots in the right ring: consider for example R[X]/(X^2 - 1). Now, 1, -1, X and -X are distinct square roots of 1.
>>16775175
X and -X aren't numbers they are variables in a formula that can be solved and the only solution for X is 1 rather than arbitrarily many as you originally claimed.
Since you don't seem to understand what a number is, is your argument just that you can come up with arbitrarily many variables such as X, X1, X2,...,Xn that all equal the number 1?
>>16774765 >- means "the other direction"
I wonder sometimes if mathematicians and physicists keep track of all the potentially conflicting meanings they assign to numbers. It does not follow that "the other direction"=-1 necessarily is compatible with the interpretation of -1 for e.g. quantum spin
>>16775130
1, 11, 19, 29, 31, 41, 49, 59, 61, 71, 79, 89, 91, 101, 109, and 119 are all square roots of 1 mod 120. Pick any ten. >>16775135
Go back to India, we have enough retards here already.
The arctan(x) (or tan-1(x)) function gives you the angle ΞΈ whose tangent is x, and this angle is always between -90Β° and 90Β° (or -Ο/2 and Ο/2 in radians).
