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  274.  @silecin  Hydrogen peroxide is a chemical compound with the formula H2O2. In its pure form, it is a very pale blue liquid, slightly more viscous than water. It is used as an oxidizer, bleaching agent, and antiseptic, usually as a dilute solution (3–6% by weight) in water for consumer use, and in higher concentrations for industrial use. Concentrated hydrogen peroxide, or "high-test peroxide", decomposes explosively when heated and has been used as a propellant in rocketry. Hydrogen peroxide is a reactive oxygen species and the simplest peroxide, a compound having an oxygen–oxygen single bond. It decomposes slowly when exposed to light, and rapidly in the presence of organic or reactive compounds. It is typically stored with a stabilizer in a weakly acidic solution in a dark bottle to block light. Hydrogen peroxide is found in biological systems including the human body. Enzymes that use or decompose hydrogen peroxide are classified as peroxidases. Properties:: The boiling point of H2O2 has been extrapolated as being 150.2 °C (302.4 °F), approximately 50 °C (90 °F) higher than water. In practice, hydrogen peroxide will undergo potentially explosive thermal decomposition if heated to this temperature. It may be safely distilled at lower temperatures under reduced pressure. Structure: Hydrogen peroxide (H2O2) is a nonplanar molecule with (twisted) C2 symmetry; this was first shown by Paul-Antoine Giguère in 1950 using infrared spectroscopy. Although the O−O bond is a single bond, the molecule has a relatively high rotational barrier of 386 cm−1 (4.62 kJ/mol) for rotation between enantiomers via the trans configuration, and 2460 cm−1 (29.4 kJ/mol) via the cis configuration. These barriers are proposed to be due to repulsion between the lone pairs of the adjacent oxygen atoms and dipolar effects between the two O–H bonds. For comparison, the rotational barrier for ethane is 1040 cm−1 (12.4 kJ/mol). The approximately 100° dihedral angle between the two O–H bonds makes the molecule chiral. It is the smallest and simplest molecule to exhibit enantiomerism. It has been proposed that the enantiospecific interactions of one rather than the other may have led to amplification of one enantiomeric form of ribonucleic acids and therefore an origin of homochirality in an RNA world. The molecular structures of gaseous and crystalline H2O2 are significantly different. This difference is attributed to the effects of hydrogen bonding, which is absent in the gaseous state. Crystals of H2O2 are tetragonal with the space group D4 4 or P41212. Aqueous solutions: In aqueous solutions, hydrogen peroxide differs from the pure substance due to the effects of hydrogen bonding between water and hydrogen peroxide molecules. Hydrogen peroxide and water form a eutectic mixture, exhibiting freezing-point depression down as low as -56 °C; pure water has a freezing point of 0 °C and pure hydrogen peroxide of -0.43 °C. The boiling point of the same mixtures is also depressed in relation with the mean of both boiling points (125.1 °C). It occurs at 114 °C. This boiling point is 14 °C greater than that of pure water and 36.2 °C less than that of pure hydrogen peroxide. Comparison with analogues: Hydrogen peroxide has several structural analogues with HmX−XHn bonding arrangements (water also shown for comparison). It has the highest (theoretical) boiling point of this series (X = O, S, N, P). Its melting point is also fairly high, being comparable to that of hydrazine and water, with only hydroxylamine crystallising significantly more readily, indicative of particularly strong hydrogen bonding. Diphosphane and hydrogen disulfide exhibit only weak hydrogen bonding and have little chemical similarity to hydrogen peroxide. Structurally, the analogues all adopt similar skewed structures, due to repulsion between adjacent lone pairs.
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  536.  @robotnoir5299  also, the axioms were designed to be as reasonable as possible. I can list them here in oversimplified form: 1. 2 sets are equal iff (if and only if) they have the same elements (axiom of extensionality) 2. a set doesn't have infinite nested sets. (axiom of foundation) 3. set builder only used to define a certain subset of a set. if you don't have this, you'll get that weird error when you make the set of all sets that don't contain themselves and the set of everything. (axiom schema of restricted comprehension)(axiom 2 also prevents paradoxes)(schema because set builder can have many different predicates an inputs) 4. if you have 2 sets, x and y, the set that contains both x and y exists. (axiom of pairing) 5. the set you get from grouping all the members of the members of a set (this set has only sets as members and those sets have sets)(basically a nested set) exists. (axiom of union) 6. the set of all outputs of a function f(x) that you can define exists. (axiom schema of replacement)(schema because there are many different kinds of f(x) (obviously)) 7. there exists a set X with infinitely many unique members (example: {1, 2, 3, ...}) (axiom of infinity) 8. the powerset of a set exists. (take a set, make a set of all sets that are like the original set except missing or not missing some of the elements)(the party bus in the video is equivalent to the numbers between zero and 1 in size which is equivalent to the powerset of naturals (the room numbers; {1, 2, 3, ...}) in size. ) (axiom of powerset) thats standard 8 in zf zfc has a ninth one 9. for all sets R, there is some binary relation X (like a < x, only compares 2 elements) that well-orders R. (well-ordering theorem)
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  657. 0:27 Yeeeee, proton! 0:50 Ok, what? Literally every company offers encryption, and you can just fake your names! Fake everything! 1:04 Yeahhhh right... They will have to turn anything in to the government if they ask. 1:19 Nice, no IP tracking! Don't they already have a VPN too? 1:35 GMAIL is encrypted. But assuming they aren't lying, yeah that wouldn't be good if GMAIL had the keys. Like, really not. 2:32 Unfortunately, approximately no one cares about encrypted things, as that's literally how every service that requires an account advertises themselves. How's proton different from the pile of junk, someone might be asking right now? 2:35 What? Oh, right. NoFunding™ does GMAIL need ads? Eh, Google gets money from the other things right? Oh, I never noticed any GMAIL promo tabs lol. mmm market pie mmmmmmmm Targeted ads don't work for me for some reason. Wait, what? How did proton mail solve the problem? Sign up failed???? Fundraising? But this isn't a solution for the problem? Proton be crashing due to fund be like:. 5:55 Paid service? Is there any reason to get it? How are users becoming products? Advertisers seem like customers though. Why the ??? would any non professional complain about 500GB- Oh, it says 500MB. Ok 1GB is bad. Proton Plus? What??? Cryptocurrencies need your wallet to be linked! 7:30 Certain crypto will still link your wallet addresses in transactions on the Blockchain, so this is irrelevant. This is the problem. Gmail is free, and is 10 times better than free Proton. No reason to switch. Also, ProtonVPN is absolutely free! Same with proton drive, otherwise where do you put the 500MB of free storage? I'm not sure what calendar that is though. 8:06 Ok, now that's good (500GB). GDrive gives 15GB for free though, and all the awful qualities of Proton Plus seem to make them force you to buy the more expensive plan to be usable? 8:22 Yup. Legit, not going to pay for privacy, when there's no reason to care unless you're a notable person who could be identified more. Google hasn't killed me yet, so why switch? What reason exactly do they have to look through my GMAIL specifically? 8:28 Yas. No way I can pay for this. The country I live in doesn't even use €. 8:55 ? What's this obstacle? Oh. Others are trained to put stuff automatically, which is why they are preferred. Convenience will always risk security. YES, there's no reason to switch all of our GMAL. Way tok many stuffs. Gamebreaking? YESS, like, the only reason I got proton M is because of the fun VPN, and I know that most people would legit not care less if they get an encryption service that has way less autofilling and way less email storage. Yep, that's why google even asks for saving passes in the first place. Proton is just way too expensive, and I would never completely switch to proton mail despite GMAIL collecting data, as GMAIL has more space. I never thought of the autofill point before this video, so there's that too. My opinion is that I'll just use proton for the funky VPN.
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  947. Okay, I haven't watched this before, let's see... 0:19 Point. 0:23 Line segment without its endpoints? 0:34 🍊 1:02 ray 1:12 vector 1:16 intersection point and that angle theorem i forgot 1:22 perpendicular 1:27 complementary angles 1:31 ratio of distances 1:39 ? 1:47 ?? 1:50 The golden ratio 1/2+√5/2, presumably the antagonist 2:08 uh oh 2:24 nevermind? right angles triangle formed 2:41 what 2:44 does it work that way 2:51 random square i guess 3:00 when is π coming in 3:07 Weird golden triangle (do notice that the angle at the top is always 90°) 3:21 How are these golden? Oh no, it's the setup to Pythagorean theorem 3:42 animation vs math 3:51 come on man, I thought this would be one of the many satisfying geometrical proofs 4:06 what? clearly 4 dimensional 4:17 Sierpinski carpet in the background... 4:37 Infinite continued fraction for the golden ratio with all the terms I guess? I assume the numbers produced when the projectiles hit are related, but I don't know 4:53 golden spiral 5:10 oooooo skateboard 5:21 RAY 5:27 golden kite (not really, a kite 🪁 looks like this, but it reminds me of a Penrose tiling, and it has all the 72° angles of any golden thing) 5:35 Triangular bypyramidal projectiles. I honestly don't have a clue what the 4D construction is, probably not a hypercube or a 5-simplex. 5:56 The pentagram/pentagon, a place where the golden ratio appears everywhere. They appear to be shooting out golden triangles (72° isoceles). I don't know what the bows are. 6:29 🍊 constructs a 4-simplex, also known as a tetrahedron. Then it's turned into an octahedron? I honestly expected him to make a 5-simplex cage fit for a 4D demon but I guess that works too. 7:04 Orange draws a cube by constructing the skew hexagon that composes a skew cube, and the corners are flush with the faces of the octahedron due to the cube (8 sides, 6 corners) and the octahedron (6 sides, 8 corners) being duals. 7:27 Orange uses the 3 golden rectangles used in the classical definition of the points of an icosahedron. This reminds me of an origami version of a burr puzzle I had.... I'm not sure if phi is constructing the icosahedron in a specific manner.... 7:47 I honestly expected this to be a 120-cell 600-cell that gets trapped in its 3D counterpart, but okay. 8:22 I guess it was the 120-cell after all, since it got trapped in a dodecahedron (which can also be formed with 3 modified golden rectangles) but why are they inside a Penrose tiling (the closest you can get to a 5-fold symmetry)/hyperbolic dodecahedron tiling now? 9:06 Well, that was anticlimactic. After watching the explanation video, I realize that it's actually a 24-cell. Okay. I also forgot to mention, but the dragon curve, a fractal, appears right after the hyperdiamond is trapped in a dodecahedron. As far as I can tell, there isn't a satisfactory explanation as to how they trapped a 4D structure in a 3D cage, but as another commenter pointed out, you can imagine it like restraining a 3D human with the 2D circles of a handcuff or the "1D" curves of a rope. They don't encase you completely, like a cage, but you're clearly not able to move. In this case, it's as if the hyperdiamond wants to move out, but a part of it, the projection in the space that 🍊 and phi are in, is stuck, and won't move. Watching an overanalysis, it appears no one comments on the numbers, and only few noticed the fractals formed when 24-cell breaks down the golden pentagon. 5:25 also, the weird kite structure made by phi is a golden "dart". Also also, phi moves the ratio in the beginning to √3. I thought this wasn't important as I'm not too good at trigonometry, but it's clear that the end result is a triangle with the angles 30°, 60°, 90°, which has a side length ratio of √3. Also also also, the colors of the different cages that are used to trap 24-cell are representative of the classical element that Plato once associated to them, the platonic solids. Tetrahedron = fire (somewhat represented here) Octahedron = air (floats in air) Cube = earth (falls to the ground) Icosahedron = water (stretches and contorts) Dodecahedron = aether (basically space, seemingly the only counter to 24-cell) also also also also, the 🍊 from Animation vs. Physics is present in the ending image, and the things visible in the dodecahedron are the 4D versions of the platonic solids with the same color scheme (aside from 120-cell/hyperdodecahedron, shown as a shadow). Fun fact, hyperdiamond/24-cell is the only one of the 6 4D platonic solids that doesn't have a 3D equivalent.
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  1116. oh my god this is the first time in 2 years I've seen someone share my sentiment that the periodic table is absolutely subject to rule 2×17 edit: ANYWAYS, potential groups of interest could just be the standard groups on the periodic table I imagine a city constructed by a group of these elementals tailored for humans alkali metals & halogens minus iodine and lithium - violent, dangers outside the city noble gases - inert, outside the bounds of this city noble metals - inert but BETTER, stay hidden for most purposes and affect things from the shadows transition metals - either explode or build the infrastructure of this elemental city lanthanides: ?? actinides & the gap of instability: radioactive dangers discussed later on Group 13 minus thallium: aluminium doing most of the heavy work Crystallogens: carbon obviously tagging along to help humanity in some way with organic compounds and stuff, silicon for the quartz and computer chips, idk abour the rest Pnictogens: nitrogen and phosphorus for explosives and more organic junk Chalcogens & alkali earth, excluding oxygen: minor guardians of the outer city specific elements?: fluorine: hell on earth chlorine: providing chloride ions while still generally disliked by the rest oxygen: violent when alone, calmed down (and possibly attracted to) the nearest metal (carbon is acceptable too :3) phosphorus & sulfur: attempt to annihilate humans via a nearby volcano but fail miserably hydrogen: WATER and nuclear fusion (tritium) helium: multiple personality disorder (helium-4 and helium-3 irl) but otherwise inert, outside the city lithium: formerly with the alkali metals wrecking havock but joins humans when the other light elements do the elements should have an age depending on when they were discovered by humanity (copper, tin, iron, etc are ancient) unrelated but I am an amateur when it comes to nuclear stuff, but I always imagined personifications of the gap of Instability (polonium through actinium) as the main enemy with thorium, uranium, possibly protactinium, neptunium, and plutonium as the main the higher actinides like americium and curium could also be enemies the stable fission products as neutral characters strontium, xenon, other dangerously radioactive ones as antagonist too
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  1234.  @fall4sleepfall4sleep26  i choose the reals, and i will now prove why the reals are more numerous. lets first state that the size of the naturals is a cardinal number, called aleph 0, or N_0 for short. next, try to show a 1 to 1 correspondence with the naturals (N_0) and the reals between 0 and 1. 1. 0.92848287373727... 2. 0.838274991873848... 3. 0.848479292841910... 4. 0.928391938488288... 5. 0.828478283838828... ... I can order the reals between 0 and 1 any way i like, because there is no way to find the next number in the reals. next, take the first digit of the first number, which is in this case 9,and add 1 unless it's 9, which it is, so subtract 1, and make a new decimal starting with that number (0.8). next, get the 2nd of the 2nd number (3) and add 1 and put it in the new string of numbers. (0.83) repeat. (0.83948...). there we go, a new number that's guaranteed to be different to ALL the numbers on the list, because we defined it to be different. as you can see, I just proved that the numbers 0<number<1 is bigger than the naturals. next, lets prove all of the reals. first notice that the reals will be the exact same form as the numbers between 0 and 1, except you put a natural at the start. (after all, the numbers between 0 and 1 are all the decimals possible, all numbers of the form 0.something) since the size of the naturals is N_0 by definition, we can multiply N_0 and the size of the numbers between 0 and 1, and by the rules of cardinal math, big infinity will absorb small infinity, and since i just proved that (size of numbers between 0 and 1) > (size of your set, the naturals), i have just proven that the size of the set R, the reals, is bigger than the size of N, the naturals. any complaints?
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