Borek
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I may have been exaggerating when I said every piece of physics, but every physicist I've spoken to or heard speak has expressed that they don't believe that our best physics theories are exactly correct (as in down to every detail and accurate on all scales).Is this true? Do you have a source or is this an opinion?
So if we take the mass of an object, and say said object is accelerating at some rate and we multiply the mass and the acceleration, we would not have the force? Is this due to an error in formula (perhaps we should subtract?), or numerical inaccuracy in measuring mass and acceleration?
I'm not really into math atm, however, doesn't that also mean that I^3=1.we can assume i^2 = -1
And either way is there no way to prove either, at least not closer than the distant future, so discussing either theory is, in my opinion, of the same level of discussing Christianity versa Buddhism; you're going nowhere.My take is that world have no choice, but to follow math. And while we can treat math as a "game of our own making" math in fact does exist on its own.
No, that means i^3 = -i and i^4 = 1. The four fourth roots of 1 are 1, i, -1, and -i. (There are four roots thanks to the fundamental theorem of algebra.)I'm not really into math atm, however, doesn't that also mean that I^3=1.
But cuberoot of 1 is only 1, not the sqrt of -1.
That told me nothing but to memorize that it's ^4 and not ^3: I did not become any wiser.No, that means i^3 = -i and i^4 = 1. The four fourth roots of 1 are 1, i, -1, and -i. (There are four roots thanks to the fundamental theorem of algebra.)
Is that because you already knew the fundamental theorem of algebra, or because you declined to learn it? I think it's a radically important part of mathematics.I did not become any wiser.
It's because I decided not to google it-- rather pray for you to explain.Is that because you already knew the fundamental theorem of algebra, or because you declined to learn it? I think it's a radically important part of mathematics.
I know the general of how exponents work, which is why I've never bothered to look it up, correct.i^2 = -1 means that i*i=-1
Then multiplying by i again gives
i^3 = -1*i = -i
You can prove that (-1)(-1) = 1 just by saying that R with the + and x operators form a field (as part of the definition of R).Well.. let's say that two negatives multiplied gave another negative:
(-1)(-1) = -1 and at the same time 1*(-1) = -1
That would imply that (-1)(-1) = 1*(-1) <=> 1 = -1 which is obviously not true.
It probably is a convention, although a convention that makes sense as we've just seen!
A polynomial of degree n with real (or complex) coefficients has exactly n roots, counting multiplicity. So there are six roots for x^6, x^6 + 3x^4 - 2x, and pi * x^6 - e * x^5 + 3.132432567. The fact that there are n nth roots of unity is just a special case of this. In the case of roots of unity, they are always distinct (unlike (x - 2)(x - 2) which has two roots, both 2).It's because I decided not to google it-- rather pray for you to explain.
Like I said before, x^y isn't exactly a function, it can have multiple, or even infinite values. It's just that a certain specific one called the principle value is taken as the value that people usually mean when they write x^y.I know the general of how exponents work, which is why I've never bothered to look it up, correct.
We never learned about exponents which is less than 1, including negative numbers, however I've seen exponents with negative numbers earlier (not @ school), but never {0, 1} or [0, 1] I forgot which one is which (never learned this @ school either, I haven't done high-school).
I just haven't done school/math in a couple of years, but yes, I realize that it was wrong twice, it should be ^4, actually without even reading the whole sentence, though my mistakes were irrelevant in both cases, so I honestly think you were going off-topic (you in plural).
i^4=1
but
1^0.25!=i
where ! means not equal to, and don't go off-topic again if 1^0.25 is wrong :P
If it's wrong, then please tell me if you want, but add a reply to what's on-topic:
I^4 is 1 but 1 4root isn't only i but 1, meaning i can also be 1 since 1*1*1*1=1 right?
2root = squareroot, 3root = cuberoot, 4root = unnamed.
Who says you have to think of numbers like you do money? Why not think of it like vector space?To DarkFire Specifically:
We are of like mind on the conceptual swallowing of a negative multiplier. Like you I see how negative values can add, subtract, and divide. But in multiplying I am conceptually snagged to see past zero as a mutiplier no matter how I try to construct it. You just can't multiply negatively. All negative values really say to me is, "its always some positive amount of negative value! No matter how I think of it I can't see past zero as the multiplier dead end. And this follows all of the math examples that try to show me otherwise. Now that said...Can I ignore my own inner concept that you can't multiply anything in this whole universe less than 1 and follow the "rule as explained", yes. But I am not at ease with it. It seems to violate some basic thought rule in me. And its one of those conceptual things I coined the "perceptual snag". I think the world is full of them. And due to natures constraints in the way we think, we are blind to them. And these perceptual snags remain invisible corrupting lots of areas of recorded thought. I think the idea of a negative multiplier is strong enough to be a "LAW". "There can be no multiplier less than the smallest fraction toward infinity. anything beyond (less than) that is ZERO! And how can you go negative (if the concept of negative is - = < 1) times "something" counted? Furthermore if you look at whats there in all negative math references you will see that even though math calls it negative, the value can always be interpreted as some Positive amount to a negative value. this of course really only applies to the "real world" value of negatives. But I can argue this point in its simplest form against any negative value.
Your "concept" about distinctive roles of multipliers and multiplicands is totally WORTHLESS, since multiplication is commutative.No you are not feeling my snag. Its not that I can not conceptualize the math rules for negative numbers. Even in vector space, its only use is as a reference below some scalier reference. At best as a concept, I still see it as non multiplier in any sense unless there is a corresponding negative value. Do you get me? Its deeper to me. Just "CONCEPTUALLY" a stand alone concept. Negative values can not be used as the multiplier. Multiplicand? Yes!