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Unfortunately, irspow, that would be 0*0, not 0^0. Otherwise, if I deposit 2 dollars 3 times, I now have 8 dollars in my account.
*slaps MathIsFun*
Everyone knows that Rom is the capital of rom.
Let me start out by saying that I try to correct people when I think they are wrong (notice the emphasis on the word think). I do it in math here on this forums, but it doesn't just stop there. I do it all the time, no matter the subject. That's all I'm doing when I reply to your posts.
Since anyone can propose a theory, why don't we make this the official "Theory's that are good, because there is no evidence against them yet forum"?
I understand this was a joke. But there is an underlying implication that I think you missed or aren't aware of. All science works this way. It's known as falsificationism. Theories are suggested, put to the test, and are either not falsified (kept) or falsified (thrown away). Now it's a heck of a lot more complicated than that, but that's the very basics of it. But to keep it simple, that which has yet to be falsified is known as "correct" in the scientific context.
Oh, and one additional requirement is that a theory must be falsifiable and testable. So no theory can escape testing, otherwise it isn't a theory.
I just never like the way they came up with the big bang theory to explain why the universe was expanding. I don't think that it is good science. Whenever some clown just decides to invent something just to explain something else that he does not understand, it just makes my skin crawl.
I don't think you know how the Big Bang Theory came about. It was first observed that spiral nebula were moving away from us. The Big Bang (although not in its current form) was proposed. Then it was observed that not only are (almost) all stars moving away from us, they are doing so at a proportional speed to their distance from us. Such evidence is only explained by the Big Bang. Then we observed cosmic background radiation. Such evidence is only explained by the Big Bang. Furthermore, it is once again only the Big Bang which explains the abundance of lighter elements in our universe.
Many different parts of cosmology are only explainable through the Big Bang. It is the unifying theory of astronomy. It is much more than conjector or hypothesis, it is a theory, just like the Einstein's Theory of Relativity and the Theory or Evolution.
And besides, as of right now, there is no other explanation which even comes close to the explanatory power of the Big Bang. We'll have to see how this new theory develops, but if its anything like every other scientific theory published in books, it will be an udder flop.
What really troubles me is that it has lasted so long now that people treat the theory as if it were reality, when the fact remains that no one knows how the universe began or if it even had one at all.
The first part is correct. The Big Bang makes no predictions as to how the universe started. All we know is that "something" happened. But we know the entire history of the universe very shortly after this something. And we do know it happened. We understand the Big Bang more than we understand the Theory of Gravity.
What I tried to say was ridiculous was the proposition that there must be dark matter and energy in order to support the unfounded big bang theory.
You may say it's ridiculous, but it turned out to be right, didn't it?
0 could be arranged only 1 way
A similar statement, there is only 1 mapping from one empty set to another empty set, also leads to the conclusion that 0! = 1.
There is only one way to map the null set to the null set. That is, 0^0 = 1. But 0^0, just like 0!, is the product of no numbers at all. So the product of no numbers at all must be 1.
I'm a Mum trying to help my son with his maths homework, and I'm not much of an Einstein.
And it's a good thing too. Didn't he fail math?
I've never seen rom either. Could we get a definition, krassi?
So, is (mod a+b) a modulus operation? And why bother if you multiply it by zero? And how can you define the product of two natural numbers to be zero?
modulo, to be exact. But it is the same idea.
k ≡ m (mod n) means that n divides k-m:
k-m = xn, x ∈ Z
So in this situation, a+b divides ab. Since a+b divides ab, a+b divides (ab)² or a²b².
Not knowing rom, I can't go any further than that.
Not weak at all, I like it.
Hey Ricky, aren't neutrinos mostly massless (as in, massless as photons, or more)?
You are correct about neutrinos. They have such a small mass that they were able to go undetected (but theoretically proposed) for 30 years. But they do have mass.
Photons, on the other hand, have 0 mass.
I thought that the dark matter theory was invented to explain why calculations (based on gravitic interactions) of the mass of the universe come out much larger than the observed electromagnetic luminosity of the universe.
Again, you are correct. Gravitational models of the universe did not correctly explain what we are seeing. So dark matter was suggested as a solution to this problem.
It seems to me that an excessively large amount of neutrinos would be required to make up the deficit, but I admit to a degree of ignorance here.
Again, right. But the one thing you seemed to have missed is that there is an extremely vast amount of neutrinos coming out of a single nuclear power plant, let alone the sun, let alone all of the stars in the universe.
And neutrinos are only one type of dark matter. Other types may exist, and here is something where I, too, have to claim ignorance. I believe matter inside a black hole may count as well, but I'm not entirely sure of that.
That does seem odd ... I guess he stands to make money if he is right or wrong.
Historically, it is those who wish to advance science that publish it in journals, and those who wish to make money that publish it in books. It is also those who publish it in books who are normally wrong.
Of course, that doesn't have to be the case here, but it certainly doesn't add to credability.
irspow, if I read something that I don't disagree with, I argue against it.
It has nothing to do with beating up on you.
edit: but let's take a closer look at my post:
First, I just asked you for some examples of what you claimed. Nothing wrong with that, is there?
Next, I was noting that we already know of dark matter that exists, something you said you didn't like the idea of. Should I not have said anything?
Finally, I agreed with your question.
So what part of that post did you think I was attacking you?
I never did like it because it seemed strange to keep a theory around which created so many results that failed to be explained by all of our current physics understanding.
Can you give some examples?
Basically, I liked the way he attacked ideas like dark matter and energy, because I too find those ideas ridiculous.
But we have even found dark matter! All three types of neutrinos are dark matter. A team of scientists (international effort) in France are building the largest particle collider which is theoretically supposed to be able to detect gravitons, another type of particle which has yet to be detected.
On the other hand, it is odd that an idea this revolutionary isn't making larger noise. No offense, MathsIsFun, but wouldn't a thoery as large as this be all over the place not needing MathsIsFun to point the way?
A better question is why are these ideas going into a book and not a peer-reviewed journal?
That's how almost all science progresses, in scientific circles. Not the public.
it's not like I sat down and memorized the trigonomic tables....hmm, I have to put that on my to-do list.
Which is only second to memorizing The On-Line Encyclopedia of Integer Sequences
.
There is a theory which states that if ever anybody discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened.
- Douglas Adams
There is a law that says it is impossible to accurately observe anything you are not independent of.
It is impossible to observe anything without interacting with it, period. For example, you can only observe your computer screen because electrons are hitting phosphorus (possibly another chemical) creating photons, which hit your eyes, change protiens in your eyes, which send an electrical impluse to your brain where even more freaky stuff happens.
But because you must change a system to observe it, you have already changed what you wished to observe and are no longer observing the previous state of the system.
Now, none of this matters until you get down to the level of trying to observe a single photon or electron. That's where quantum physics comes in.
The following quote is from Dave W. at the SFN, which I now also share:
Time to whip out the Crackpot Index again, only because of the guy's style. There are a whole bunch of points right on the main (short) Web page, and he starts out talking about how long he's been working on his theory! Why is he doing lectures and writing a book instead of publishing articles in the appropriate journals? Why is he citing unpublished work?
Emphasis from the original.
I am exteremly skeptical, especially when it comes to:
A number of outstanding scientific mysteries are definitively solved, including observations that lead to the concepts of 'dark energy' and 'dark matter'.
But I'll have to read all the pdfs/powerpoints in great detail before I can comment further. It might take some time.
Yes, but why are you saying the changing lenght of the blade complicates the problem? Those functions describe that change.
Well, the way I read it, the functions given by the question are describing the changing length of the blade. It does change, after all, but it is 3cm off from 20. Is the 20-30cm change just supposed to be approximate? If so, then the equations as stated properly represent the area of integration. If not, then there may be some oversight in assigning the functions or 120° by the creator.
Or the function don't represent the changing lenght of the blade, in which case I believe this question is impossible.
I'd rather go with the first option personally.
My argument tends more to a philosophical level. Philosophical arguments, er debates, can only be won when one of the contributors is willing to change core beliefs. In my case that will not happen on this subject.
That's fine, but we can't just talk about it?
I think that all types of definitions just represent the limit of understanding at the time in which they were created. So I feel to defend definitions simply to protect the status quo is silly.
And just to reiterate, I think that definitions are the same as us calling a sock, a sock.
Can't we agree to disagree? I am not here to debate anything, so I probably should not have offered my viewpoint in the first place.
Sure we can. But even if we do so, we can still discuss why it is we disagree. And like I said, if you don't want to debate about it, that's fine. But your viewpoint is always welcomed.
Actually this type of discussion is not even appropriate in a math forum anyway.
Sure it is. It's about math, isn't it? So what if it's in a philosophical context.
Oh, I did not attach any negative connotation by using the word zealot. There is no such one implied in the definition provided either. I used it in its strictest sense only.
Zealot sure does have a negative connotation. And besides, look how you used it:
of the zealots who serve to protect [pseudoscience]
You're talking about zealots who protect pseudoscience in reference to me. If that doesn't have a negative connotation, I'm not sure what does.
And shouldn't the y3(right boundary function) be y = 40 - x/:raic3?
Yep. Big mistake on my part. Nice catch.
When I find the length of the wiper blade based on my functions (with the √3 change), I get the blade goes from 23.5307 to 30cm. Not exactly 20-30, but close. Is the question wrong? Is the interpretation of it? Not sure.
I guess I underestimated the level of indignation that could be aroused at the mere mention of a differing idea.
It's not that you are mentioning a different idea, it's the idea that you mention and how you mention it. And calling me a zealot just because I disagree with you only makes you the zealot.
All you said in that last post is that I disagree with you. I, on the other hand, have been saying why I think you are wrong. Please, do the same to me.
The definition of science does include the interpretation of it as skill set for solving problems.
Science, the most basic definition, is the study of our natural world. Math is not part of our natural world. It can be used as a tool to probe into the universe, but it is not a part of it. Ironic that it was the Pythagoreans who believed math was a part of our natural world...
If you don't wish to reply, I'm not pulling your leg to make you do so. If you want this conversation to end, that is fine. I, on the other hand, love debates, especially when I'm right (just to be clear, that was a joke). But I implore you, if there is one thing you get from this, it is to argue appropriately.
They laughed at Newton, they laughed at Galileo, but they also laughed at Bozo the clown.
I have dealt with pseudoscience for the past 3-4 years of my life, being a skeptic. Homeopaths, psychics, ghost hunters, you name it. One of the few things that unite all of these groups is what you just did in your previous post. Claiming that you were silenced ("executed") because you proposed a new idea. When this happens, a huge red flag appears in my mind.
It is this argument that comes from those with no other arguments to go off of. Please, don't make it. You know I'm not trying to silence you. I'm trying to have open discourse, I thought that's what this forum was for.
If you think I'm wrong, then state why you think I'm wrong. Point out what you think are errors in my posts. But, if you're not sure why you think I'm wrong, but you still do, then just say it. I have been in that situation many times. There's nothing wrong with it.
I already have basic differential and integral calculus down and am starting to learn abstract algebra.
I'm in the same boat. Kind of weird how after doing a few years of calculus you go back to proving why -1 * -1 = 1, isn't it?
It is a dark day in any science when its followers vehemenently deny the possibility that other foundations would perhaps advance their understanding of truth.
Yes, it is. Good thing no one else but you is even talking about science.
It is an even darker day when its followers would prove the validity of their theories by simply stating that that is the way they have defined truth.
What? We aren't defining truth. We are defining ideas. What is a prime number? Prime is a definition. If you wish to call it something else but prime, or if you wish to call a wigglysnug something that is divisible by itself and one, you may. But there is no point. Names don't mean anything, they just make it easier for us to express ideas.
The Pythagoreans elevated their mathematic science to the level of a religion.
Is anyone else here agreeing to that philosophy? Then why bring it up?
Irspow, we aren't talking about truth. There is no truth value of "any number that is divisble by only 1 and itself." You can't say true or false to it. It's just a type of number. Will that type of number ever change? No. Even if we call it something different in the future, or if we call something else prime, that type of number will still exist.
The same is true for all definitions. Whether it be a function, operation, group, set, field, irrationality, even, odd, and so on. It's just what we call things that have certain properties.
irspow, I'm not understanding your objections at all.
The problem gives two curves and two lines, and want you to find the area inbetween all of them.
What's wrong with this?
What we percieve as 1 is really quite different from reality.
How do you percieve 1? 1 is an idea, not a thing.
Being that we do not know our position relative to the true planes or even that they exist would continue to force us to make incorrect assumptions about what we perceive to be fact.
1 + 1 = 2. This is because of how I define 1, 2, + and =. It has nothing to do with my perception of them. If I defined them differently, 1 + 1 ≠ 2, but definitions are just want we call things. They are arbitrary, just as arbitrary as why I call my pet a dog.
In this example, something that we observe to be a singular object at a specific place would indeed be two different objects at two different places.
Since when are there objects in math?
I am not here trying to disprove any of the concepts that some place in the sector of sanctity, but rather to point out that there is always the possibility of other interpretations of the truth.
I understand where you are coming from. I share the same view as you, except that I only apply it to science. It doesn't seem to apply to math.
There can be "revolutions" as people discover whole new territories, but the existing knowledge does not get invalidated.
That's not entirely true, if read literally. But I believe what you were trying to say is this:
If math is done correctly, the results are final. No amount of time will over turn the results of a correct proof.
This is different than science in which you can do everything correctly, and still come up with an incorrect theory.
Oh, ok, I misunderstood you before irspow. But I'm still not sure what you mean now:
Sooo, what are the proper limits of integration for y1 and y2?
What do you mean limits for y1 and y2? My solution never integrates y1 and y2. It integrates y1 - y2, is that what you mean?
If so, the limits are b to c.
b = intersection between y1 and y3
c = intersection between y1 and y4
√(2)x + 40 = 1/50x^2 + 30
b=-5(√(35)-5)*√(2) or -6.47766
1/50x^2 + 30= -√(2)x + 40
c=5(√(35)-5)*√(2) or 6.47766
so you integrate y1 - y2 from ~-6.5 to ~6.5
To sum up for Jonny, the answer (so far) is:
y1= 1/50x^2 + 30
y2= 1/50x^2
y3= √(2)x + 40
y4= -√(2)x + 40
a = intersection between y2 and y3
b = intersection between y1 and y3
c = intersection between y1 and y4
d = intersection between y2 and y4