I hope this was more of a study than just asking people what they think "the coffee is not hot" means. To me this sounds like a bit of a self-fulfilling prophesy rather than science. Did they study how people react to "this integer is not even" or "this sentence is not false" or "a deck of cards is split and one half does not have the ace of clubs"?
Also, I hope the researchers know about Demorgan's theorem and that if you have the set of integers from 1 to 100 and x is not 100, then x could be any other number. Obviously, if the coffee isn't hot it's somewhere between warm and cold.
A bipartite graph doesn't need to be connected. Thus, you won't prove that a bipartite graph is connected.
To answer the question though, suppose G is a bipartite graph. Let u and v be any distinct vertices in G. Suppose (1) there exists an odd-length u-v path P and an even-length u-v path Q. The walk starting on u, going through P, stopping at v, going through Q, and ending at u is a walk with length parity 1, because we went through an even path and an odd path. We have a closed odd walk, which has an odd cycle. You seem to be good with the fact that a graph has an odd cycle iff it's not bipartite. Thus, G is not bipartite, that's a contradiction, and (1) is false. The negation of (1) is your statement "G has the property that for every pair of vertices u, v we have that every u-v path is of even length or every u-v path is of odd length." Thus, we showed that your statement is true if G is bipartite.
I think the missing effort here is showing that a graph is bipartite iff it has no odd cycle. There is a bit of work involved, so perhaps you should explicitly state whatever we are taking as given. Why is it that a graph with no odd cycles is bipartite?
It looks like
(1) being bipartite
(2) for all u, v in V, (every u-v path is odd, or every u-v path is even)
(3) having no odd cycle
are all logically equivalent. I'll double check this later.
Mathologer gave the simplest explanation. Just like you can create a bijection from the set [0, 1] to the set [0, 2], both being subsets of the real line, you can create a bijection from all points in a sphere (including the enclosed volume) in to the set of all points in the union of two disjoint spheres (including the enclosed volumes). I could also call these closed balls. Knowing this, the paradox is actually an expected result.
You would fool no one. The veteran debunkers have been at this for about 9 years, and can easily tell if someone is just pretending to be a poe with no knowledge of the "debate". Also, they want to send a flat earther with a following, such as Witsit, David Weiss, or Jeranism. These 3 flerfs will be strongly encouraged to take the free trip as this is the whole point of the investment.
There's a list of 24 globers and 24 flat earthers who are already chosen. They want someone well-known to go, and this is kind of the point, as plenty of people have already been to Antarctica to see the 24h sun and the flat earthers believe exactly 0 of them. The whole point is to send a flat earther down, and have a well-known glober to be there with them.
I don't think I'll ever be able to figure out what he means. Cranks can't answer simple questions. The guy who shared this meme says "the earth's not flat", but he also strongly believes "all horizontals are parallel" (where a horizontal is a plane that intersects exactly one point on a sphere and is tangent to the sphere at that location). He's a flat earther in denial, but all he ever says when you ask what he means when he says "Earth's not flat" is "it has hills and valleys." I was in conversation with this guy and he talks very, very, painfully slow. He takes about 5 seconds to say the word "horizontal."
"2. Or disjoint means the elements within each of the sets themselves, and since 1,6 are connected it's not" isn't a sentence.
I suggest you go hang out with the flat earthers, since they will likely share your view and be open to hearing from you.
Restate it to be a bit more logical. "If someone is a sore loser, no one likes them." More explicitly, "if someone is a sore loser, there doesn't exist a person that likes them."
Your statement is "every person is such that they are a sore loser and no one likes them. From that it follows that everyone is a sore loser, but that's not true of all universes. The "for all" quantifier distributes over AND statements because the "for all" quantifier basically creates a giant AND statement (saying "element 0 is this, and element 1 is this, and element 2 is this, and ..."), and AND is associative.
Multiplying a pair of matrices, each with more than 1 row and more than 1 column, is not that hard. If you have matrices A and B, then AB can be found by thinking about the familiar Ax = b equation where x and b are column vectors. Split B up into its columns, for each column x take the product Ax, and then B is simply each of those columns in order in a new matrix. Instead of one column, b, you have a list of columns, B. Previously, I had imagined taking B, rotating it counterclockwise 90 degrees, and overlaying it on A, and memorizing where each dot product went.
You really should update the FAQ to answer that the temperature should be at most 15degC. If someone lives in a climate that doesn't let the water get that cold, they'll either have to accept it or find some other way to get the water colder.
I do this only for the benefits. If cold showers had no benefits I wouldn't take them.
I think the form where you enter your email indeed proves that he is gathering data. Forms are for gathering data. I don't know what he's doing with it besides emailing me something that he could have just posted directly to a website. However, when I see a random link coming up asking for my email, that's a red flag.
I don't see why Richard needs my email. He could just post the stuff on his website. I don't really approve of data gathering under the guise of activism.
I think he did a good thing, even if he lied. Turning people away from this processed, unhealthy food is a good thing, and we need to switch to plant-based diets today to reduce greenhouse gas emissions. The meat and dairy industry is also cruel to animals. In logic, "false implies true" is a true statement, so even if he reached his conclusion from a false premise, his conclusion can still be correct, and it is. We shouldn't eat this stuff.
I know very little about it, but I've heard about the garbage waste that ends up there. There are many mountains around the world, but "I need to climb Mount Everest for my social status." A lot of these people should find a different mountain to climb. The question to ask is "why do you need to climb Mount Everest?", and further questions should be asked to see what the real reason is.
I asked about that (here ) and I ballparked it a 10 trillion Joules/sec (assuming the energy I calculated was added over 100 years). Looks like my very rough and oversimplified calculation was only an order of magnitude or two off. Hopefully this way of expressing it will wake people up and make them realize that something needs to be done.
They are just telling you to vote, not who to vote for. There's nothing on the pamphlet that says "vote for Trump." It just says "vote."
Ask what the teacher is looking for then. Clearly, (9)(10.5)+16 is 110.5. I don't know if your teacher means that you have to round up to the nearest integer, so that 9.02 hours rounds to 10 hours, because if you round down then technically you don't have enough money. I'd ask the teacher at this point.
A previous answer I gave answers this question: https://www.reddit.com/r/learnmath/comments/1cod6yp/comment/l3dbyfl/
The Struggle in Learning Math from Scratch
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