Mathematical

Is there a forum or subforum for long-form discussions which ideally avoid the nutty people who can't write a proper sentence or paragraph? I ask, because if not,then it would make a great place to ask certain kinds of questions, and provide well reasoned answers rather than paragraph long quips.

lol

Yeah, the Irony really seems to be lost on him. So you're saying in order for two people to communicate, they must have both the means, medium, and nouns to generate a communicable idea? What a miraculous idea, it's almost as if you could have said that in a sentence and no one would have disagreed with you, but instead you persist to communicate as if you are talking to a near nonexistent audience and write your ideas in the same format as a technically illiterate grandma and with the same flow as a an email with the subject "FW:FW:FW:FW:RE:FW:FW:FW:RE:LOL YOU GOTTA LOOK AT THIS, I GOT THIS GUY SO HARD" You're not even going to try to elucidate us mere mortals to your magnificent breadth of wisdom over this topic? Such impressive communication skills.

Except gravity doesn't propagate faster than light. Gravity propagates at the same speed light does, c. If it helps, you can think of gravity as being the same thing as light, but gravitons instead, however there has not yet been any evidence such particles exist, as of yet.

I assume you're asking because of the observer causing the probability wave to collapse, otherwise known as the observer effect? Let me make one thing clear, there is no reason to think or assume that consciousness has anything to do with this phenomenon. With that in mind, whether it were a plant or a human doing the observing, it wouldn't matter. I should say it shouldn't matter, but I know of no reason why plants would make any more of a difference in the double slit experiment over other means, that being said I know of no research on the matter to direct you towards. If I am wrong in my interpretation of your question, I am happy to correct my response or otherwise retract anything I have said here.

Why is it that at the first moment of a genuine assault on a person's political candidate of choice, rather than either defending the individual's statements, or establishing that said statements were not false, their first response is to attack the next leading candidate? I have absolutely no shits to give about Hillary, I do about Trump, yuhknowbeingthepresidentandall.

Simple answer. No. Longer answer. God fucking dammit, why do people still take these obviously bullshit ideas with anything other than the largest fucking grain of salt that it would make a salt plateau look like a fresh water lake, for Satan's sake, NOOOOOO. Real answer. If you read something, and that thing has something happening in it that is the equivalent of, or similar to: time travel, teleportation, mind reading/control, full invisibility (as opposed to partial or illusions), ghosts, demons, gods, or any other manner of "too good to be true" scenarios, then it's probably bullshit. If you're not getting this information from a respected science news site, or an educated professional, then you're being fed misinformation. So, to answer your more interesting question, no. Firstly, electromagnetic waves are light, kinda. Rather, light is one particular version, but the other is magnets and electricity. At least that's the case, if I am being brief. There's a lot to cover, but I digress. Light and magnets can affect your brain, but they cannot make you remember things you didn't experience, or control you. They can't make anything teleport any distance, especially a warship. Secondly, I ask you this, if this technology ever existed, even if it is magicvoodoosciencebullshit, why was it's first test on a war ship, and not something smaller and less expensive? Where are the applications of said technology today. No government or military will simply lock up such a technology in a vault. They'll use it. Where are the bombers incapable of being detected by any radar system? Where are the teleporting bunker missiles that don't even need planes to get to their destination? Where are the non-military applications? Windshields that never need cleaning, exceptionally awesome vacuum chambers? 99% of said, or similar stories I can ask these same questions and comfortably tell you with over 99% confidence that it never happened and is absolute horseshit. A simple google search for "philadelphia experiment debunked" should turn up a variety of sources, including videos, blogs, and genuine researched and sourced articles. A few minutes browsing turned a few sites up, but I will not link them here due to their dubious nature. In short, if you think something sounds dumb, it probably is. Check a variety of sources, check their sources, and digest the information you learn. If you come to the conclusion that such effects are still real, then there may be some legitimacy to the claim. As for physics information, there are a variety of educational sites which will provide the needed information, but if you want to really learn it, then school is your friend.

I am guessing you've recently learned about the simulation theory of reality and are looking for a genuine answer to the question, and because of your general, and probably limited, knowledge of physics and mathematics (God knows I want and need to grow mine further still) you feel there is probably an answer hidden in a textbook somewhere and you've thought somethings along the lines of "Maybe one of the guys on a forum dedicated to science has read the answer, but it's just not well known". Hate to break it to you, but a moment of critical thought about the idea would reveal that no, there is no such answer and there couldn't be. First of all, let's break down your question, I first want to point out embedded in your question is another question about the definition of real, existence, and imagination. We can all agree that the building that the senate uses does exist, but in what sense does the senate exist? When you see the building, do you see the senate, or just the building it uses? When you walk in, and watch the votes, are you seeing the senate, or just a bunch of guys in a room? When someone casts a vote, does the vote exist, is it synonymous with a scratch of graphite on a piece of paper, or does the vote hold something which the graphite doesn't? Embedded in all those questions, and more, are the questions "What does it mean for something to exist?" and "What does it mean for something to reasoned about?". Neither of said questions has an easy answer, nor an agreed upon answer by all people everywhere. Your answer to those questions actually reveals a lot about who you are as a person, not to mention the scale and depth of your thought and consideration for such matters. Moving on... Assuming for a moment that we did have a perfect answer for the previous section, one that we could all agree on and was definitely correct (Spoiler: nope), it's clear you have litter understanding of what an equation really even is. Generally an equation is a statement of equality, one thing is the same as, or similar to, another. [latex]a=a[/latex] not because it's just some axiom we take to be true, nor just because math wouldn't work without it, but because reason itself would not exist. Oh sure we can always add extra layers of complexity to our answer, and say things like either this thing is true, OR we get something we don't like or it isn't very sensible, or we have to throw away this whole other thing that we also really like, but at the end of the day, those answer boil down to it is or there is no reason to be found here. With that in mind, you want to basically know if there is an equation that looks like this: [latex] T = exist?(thing) [/latex], where T is the logical value True, and only things that do exist will satisfy the equation, and things that don't will result in a contradiction, much in the same way that only answers to [latex]y=x[/latex] are points on a straight line at 45 degrees to the x-axis. So this part comes back to the previous section, you must first define what it is for something to even be real before you can even write an 'equation' to answer that for us. Eh, I was going to continue, but at this point, all of the rest of what I can say would either be extremely presumptuous or simply "you still have to answer that first question before you can even move on" and I am bored now, so I am done.

I have no idea what you are arguing or pointing out. Yes, the density of primes decreases in the subset, [latex](0 , n)[\latex], of the integers decreases to zero as your right bound approaches infinity.

Not anymore, I was trying to put into words what I was thinking, and had gotten it in my head associativity implied commutativity and visa versa. I was trying to get my reasoning in a form I could more easily criticize, and after I had done so, I had remembered matrices. As such, I simply edited the post, and made it clear that I was wrong, and it should have been clear there was no need for any further discussion. However, that seems to not be the case, so let me be clear: I was wrong, and there is no further need for discussion.

You're thinking of the Sieve of Eratosthenes. I mean, you literally just stole the name, then replaced it with your own. Nothing you did was new. To make matters worse, you clearly lack any meaningful understanding of the topic, because your writing is as rambly as mine is when I am writing and thinking about a brand new topic to myself. I literally did the same thing last night with regards to fundamental algebra, associativity, and commutativity. The sieve, as you mentioned, is formed by starting with two, marking it as prime, and then marking all the integer multiples of two as not prime. Then you proceed to the next number that isn't marked, if no number below it multiplies by an integer to yield it, then it is prime, and you mark off all integer multiples of that, then proceed to the next unmarked number. Following those steps, you get the primes 2, 3, 5, and 7 rather quickly, you immediately mark off all evens, multiples of three, five, and seven. To top it all off, as showcased in the first image on the wikipedia, by following those steps you've already found all primes up to 113, inclusive. In addition, your statement that the composites are distributed "in the same way as primes", well, actually all composites are spread in the exact opposite manner, since primes become less dense as you go up the number line, then composites must necessarily become more dense. In other words, your description is patently, obviously, false. In short, if you want to be taken seriously, proof read and google the hell out of your idea. If you think your idea is ground breaking, and you're not a professional mathematician on the bleeding edge of knowledge, it's probably not. God knows I've made that mistake plenty of times.

So, I was looking into fields and was studying up on them, and noticed that associativity seems to be a rephrased version of commutavity. For a set [latex]S[/latex], with operations [latex]*[/latex] and [latex]o[/latex], and given that the set is commutative, but not necessarily associative, we can rephrase the question of associativity like so: [latex] a * (b * c) = (a * b) * c \implies (b * c) * a = (a * b) * c \implies (b * c) * a = (b * a) * c [/latex] This is rather obvious, especially if it is associative, but we can still phrase it differently: For a given [latex] b [/latex], where [latex] x|y = (b * x) * y [/latex], is [latex] | [/latex] commutative. In other words, associativity implies commutativity, but commutativity does not imply associativity. --- Is my reasoning erroneous? Is there something I am missing? never mind. Matrix multiplication... FFS. How did I forget that. I even double checked that myself the other day.

A functional average? As in the average of a function over an interval? Can you explain more clearly?

So let me get this straight, because I want to make sure I understand what you are asking, you want to prove that given some function, [latex] f [/latex], continuous over [latex] [ a , b ] [/latex] that there is some [latex] x \in [a,b] [/latex] such that [latex] \int_a^x f(t)dt = \int_x^b f(t)dt [/latex]? If so, this is the same as asking for any area, can I divide it in two (with a straight line), such that both sides have equal area. The answer is clearly yes, in fact the intermediate value theorem necessitates that this is true. Like you wrote, the simplest way I can think of to find x is to do what you did, [latex] \int_a^x f(t)dt = \int_x^b f(t)dt \rightarrow F(x) - F(a) = F(b) - F(x) \rightarrow 2F(x) = F(b) + F(a) \implies x = arcF( \frac{F(b) + F(a)}{2} ) [/latex] If you want to prove that it is true, then I'd use this method: IVT states that given some [latex] c \in [f(a),f(b)] [/latex], assuming the function is generally increasing over our interval, then there is some [latex] u \in [a,b] [/latex] such that [latex] f(u) = c [/latex] Changing the names to match our problem yields If there is some [latex] c \in [F(a),F(b)] [/latex], assuming the function is generally increasing over our interval, then there is some [latex] x \in [a,b] [/latex] such that [latex] F(x) = c [/latex] Since c is exactly halfway between [latex] F(a) [/latex] and [latex] f(b) [/latex], then we've proven that there is some [latex]x[/latex] that satisfies our conditions. Replacing [latex]c[/latex] with [latex]\frac{F(a)+f(b)}{2}[/latex] shows us that the formula that you came up with is exactly the formula that you need to find x, and while you might be able to find other such methods, this is probably the simplest out there. I just want to point out that you meant [math]x= \frac{1}{\sqrt[3]{2}}[/math]

My goal: Write a python script that will hold the left set, right set, and calculate the value of a surreal (if it is finite) and return it when called. As I understand it, a surreal number [latex]S[/latex] and [latex]S'[/latex] are equvalent so long as the the maximum of the left sets, and the minimum of the left sets are the same or simply: [latex]S=\{S_L|S_R\} \equiv \{max(S_L)|min(S_R)\} = S')[/latex] [i cut everything else out, because I wasn't making sense, please see below] For fuck's sake, I hate this unnecessarily complicated recursive numeral system. THIS is why more people don't understand surreals, because the numbering system isn't intuitive at all. Can someone please tell me how I can find the value of a given [latex]S[/latex]? --- def calcvalue(self): if self.rightisempty and self.leftisempty: return 0 elif self.rightisempty: return max(self.left)+1 elif self.leftisempty: return min(self.right_-1) else: return (max(left)+min(right))/2 Also here's this code. Is this accurate?

Well, thank you everyone! Really. Unfortunately, I cannot retrieve the lost content and will write it up again later.

Gah... I thought I was safe because it even said "Post autosaved" in the bottom left of the editor when I previewed the post. Damn.

SHouldn't the editor autosave my post? Where can I find it?

I wouldn't say that, personally. Any questions you ask about fundamentals, be they a god, or some other fundamental truths of reality necessarily turn to questions of epistemology and nihilism. So these questions of some fundamentals turn towards other fundamental questions that are, by their nature, unanswerable, or if they are, unknowable, at least, without some set of assumptions.