What is the mistake in this mathematical proof? | AskScience Blog

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Wednesday, February 15, 2017

What is the mistake in this mathematical proof?

What is the mistake in this mathematical proof?


What is the mistake in this mathematical proof?

Posted: 15 Feb 2017 02:08 AM PST

From Hexaflexagons and Other Mathematical Diversions by Martin Gardner

a=b+c

multiply both sides by a-b

a2 -ab=ab+ac-b2 -bc

move ac to the left

a2 -ab-ac=ab-b2 -bc

factor:

a(a-b-c)=b(a-b-c)

divide both sides by a-b-c

a=b

He says that this is a fallacy, but can't you just say that c=0?

submitted by /u/Booty-Zipperooni
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In a nuclear weapon, how do the explosive lenses create a supercritical mass out of a subcritical mass, when the actual mass of the fissile material remains the same?

Posted: 14 Feb 2017 08:58 AM PST

Say you start with 3kg of plutonium in a hollow sphere shape, prior to detonation. After the explosive lenses are detonated, you (very briefly) have a solid sphere of plutonium created by the explosion. However the mass of the plutonium is still 3kg - exactly the same as the original mass. So I guess my real question is this: is the term "critical mass" a misnomer? Should it be instead, "critical density", or "critical mass per unit volume"?

submitted by /u/musicmunky
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In Quantum Mechanics, why is the de Broglie–Bohm theory (Pilot-Wave theory) not as popular as the Copenhagen interpretation?

Posted: 15 Feb 2017 06:56 AM PST

My understanding of these interpretations is pretty slim overall, so please try to ELIinHighSchool. I don't understand why the modern Pilot Wave theory isn't as accepted as the Copenhagen interpretation when it avoids paradoxes such as Schrodinger's cat. If you notice that I have some kind of misconceptions of these theories please clarify them for me. Thank you in advance!

submitted by /u/Runedweller
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Ask Anything Wednesday - Engineering, Mathematics, Computer Science

Posted: 15 Feb 2017 07:05 AM PST

Welcome to our weekly feature, Ask Anything Wednesday - this week we are focusing on Engineering, Mathematics, Computer Science

Do you have a question within these topics you weren't sure was worth submitting? Is something a bit too speculative for a typical /r/AskScience post? No question is too big or small for AAW. In this thread you can ask any science-related question! Things like: "What would happen if...", "How will the future...", "If all the rules for 'X' were different...", "Why does my...".

Asking Questions:

Please post your question as a top-level response to this, and our team of panellists will be here to answer and discuss your questions.

The other topic areas will appear in future Ask Anything Wednesdays, so if you have other questions not covered by this weeks theme please either hold on to it until those topics come around, or go and post over in our sister subreddit /r/AskScienceDiscussion , where every day is Ask Anything Wednesday! Off-theme questions in this post will be removed to try and keep the thread a manageable size for both our readers and panellists.

Answering Questions:

Please only answer a posted question if you are an expert in the field. The full guidelines for posting responses in AskScience can be found here. In short, this is a moderated subreddit, and responses which do not meet our quality guidelines will be removed. Remember, peer reviewed sources are always appreciated, and anecdotes are absolutely not appropriate. In general if your answer begins with 'I think', or 'I've heard', then it's not suitable for /r/AskScience.

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Past AskAnythingWednesday posts can be found here.

Ask away!

submitted by /u/AutoModerator
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If liquid helium is the coldest substance we have commercially available to us today, how did we first cool helium down to that temperature without the use of something colder?

Posted: 14 Feb 2017 04:16 PM PST

What would the evolutionary benefits be for male mammals' testicles being located in such a vulnerable location instead of being inside the body?

Posted: 14 Feb 2017 06:33 PM PST

Being such an important organ (perhaps most important, considering an animal's ultimate goal in life is reproduction) what would/could be the reasons why mammals have not evolved in parallel to have testicles located in a much safer location inside the body rather than exposed in the way they are? I just noticed the obvious vulnerability of the organs as I am watching the AKC dog show right now, and every male dog has incredibly vulnerable jewels. Thanks!

submitted by /u/g_eazybakeoven
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Does the diffusion current have an upper limit?

Posted: 15 Feb 2017 02:40 AM PST

What happens if I completly compensate the built-in voltage of a pn-junction? There should only be a finite amout of current, due to the finite amout of electrons/holes right?

If anyone has a satisfying answer I would be much obliged.

submitted by /u/Allimania
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What's the highest frequency laser?

Posted: 14 Feb 2017 05:58 PM PST

I've been playing the game Stellaris which has a late-game technology you can research, gamma-ray lasers, which got me thinking about laser frequencies.

The wikipedia page for gamma-ray lasers certainly makes them sound like a difficult research project, not something in production. The graphic they have for commercial lasers by frequency seems to imply the highest-freq commercially available laser is pretty solidly ultraviolet. Are there higher-freq research laser, and if so, what are they used for?

Is the trouble in producing higher frequencies finding an appropriate gain medium? If so, what research is there in finding such materials? If not, what IS the main obstacle?

Further questions: if we had such a laser (gaser?) what would be some of the research, industrial, commercial, and military applications that we couldn't do with a UV laser? In particular, would this have applications in laser fusion?

Also, searching this subreddit, I found this question about doubling a lasers frequency, which doesn't sound that hard in the thread. Could this method, or some other method of raising a lasers frequency, other than the brute force approach of just accelerating the emitting device relative to the target, be used in production of a high-freq laser? How does this apply to the above?

submitted by /u/zelmerszoetrop
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I recorded some electromagnetic fields, is what I am seeing in the spectral frequency the pulses of electrical communication?

Posted: 15 Feb 2017 02:16 AM PST

http://imgur.com/a/hZEyK

I was wondering what these lines are in the spectral frequency viewer

Here is the recording - http://www60.zippyshare.com/v/tXLQQLeY/file.html

is a recording from a modem router, monitor, speaker, lights. just stuff in my room.

submitted by /u/ni-ten-ichi-ryu
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What is it called when snow forms a very light crystalline layer on the top? And how is it formed?

Posted: 14 Feb 2017 02:16 PM PST

I was in Utah and went snowshoeing when I noticed that the top layer of snow was formed of millions of small crystals. It almost looked like really short grass made of ice was covering the snow. It reflected a rainbow of colors as I looked around. I wanted to know more about this phenomenon so I could learn more about it.

submitted by /u/im_not_my_real_dad
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Does orbital localization in a molecular wavefunction imply time dependence?

Posted: 14 Feb 2017 08:58 PM PST

This may get somewhat lengthy... but I've been wondering about a few properties of localized orbitals in molecular wavefunctions. It is typically argued that any arbitrary unitary transformation can be applied to canonical orbitals, because such a transformation will leave the overall wavefunction and all observables unchanged. This is typically accompanied by the interpretation that there is no "best" way to set up the orbitals, and any set obtained from a unitary transformation is as good as any other. However, that actually raises two questions for me.

  1. Let's assume we obtained a wavefunction from a typical Hartree-Fock calculation. A localization procedure will generally form linear combinations of canonical orbitals (thus, eigenfunctions) to different energy eigenvalues of the Fock operator. But doesn't that mean that the localized orbitals are basically a superposition of eigenstates, which is not a stationary solution to the (time-independent) Fock operator anymore? Nobody talks about localized orbitals as a time-dependent concept, which makes me feel that my assumption may be wrong for some reason.

  2. Tapping into an old battlefield of MO and Valence Bond theories: Some people like to use the photoelectron spectrum of methane to highlight the correct symmetry behavior of the canonical molecular orbitals. This symmetry is obviously broken if we localize the orbitals in order to willfully represent four equivalent C-H bonds. So, my question is: How does the argument uphold that any unitary transformation leaves the orbitals just as viable, if localization can introduce such an obvious contradiction to reality? Would a time-dependent interpretation as a non-stationary superposition state be able (or perhaps, even necessary) to reconcile theory and experiment?

submitted by /u/RapidCatLauncher
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Why do the "biggest stars in the Universe" basically all appear in the Milky Way?

Posted: 14 Feb 2017 05:18 PM PST

I was looking at a list of the biggest stars in the universe and they were all relatively close to earth. It doesn't seem possible that with so many stars in the universe, most of the largest ones would be located within our own galaxy.

Can we not see stars in other galaxies?

Obviously I know these are just the biggest stars that have been observed, and that this is not a definitive list, but something doesn't make sense to me.

submitted by /u/harrybro
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How does the fusion of 4 hydrogen atoms create helium and not beryllium?

Posted: 15 Feb 2017 04:50 AM PST

At about 8min15sec in this video, we are told that 4 hydrogen atoms going through nuclear fusion creates a helium atom. Why is it not beryllium if there are 4 protons?

submitted by /u/dilirst
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At what point does the first radio signal from earth just become an indistinguishable part of the background?

Posted: 14 Feb 2017 03:27 PM PST

Given the strength of the first radio signal, how far did/will it go in space without dissipating to the point where it is indistinguishable from noise?

How have modern signals changed to differ in their longevity in terms of viable distance traveled, and why?

submitted by /u/AnArmyOfWombats
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Why does the Wu experiment prove that parity is not symmetric?

Posted: 14 Feb 2017 10:26 PM PST

I believe I understand the experiment, that the magnetic moment of Co60 atoms were lined up in the same direction, and the direction of electron emission during beta decay measured.

What I don't understand is why this proves the universe has a handedness, and not just that the weak force and magnetic moment are interrelated, or some smaller structure influences both the weak force and magnetic moment.

I mean, given a changing electric field, you can predict the direction of a magnetic field, but all that means is that they are aspects of the same process, not that some basic quantity isn't conserved.

submitted by /u/MapsAreCool
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Is it possible for Hubble to image Voyager?

Posted: 14 Feb 2017 04:00 PM PST

Why is it when you handle some foods (like onions) the smell will stay on your hands for several hours, even if you wash your hands more than a couple times?

Posted: 14 Feb 2017 02:23 PM PST

Are neutrons the only things that can actually physically touch?

Posted: 14 Feb 2017 02:03 PM PST

I know people can't actually ever touch each other, they just feel the repulsive force of electrons on a macro scale. Since neutrons have no electromagnetic attractive or repulsive force, can they actually fully come into contact?

submitted by /u/ThatTallDude326
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Do magnetic fields carry information?

Posted: 14 Feb 2017 07:08 PM PST

I know that radio waves (or any EM radiation) generates a magnetic field along with the E field, but I cant find out if the magnetic field somehow carries that same information. (for example, would the magnetic field of a radio transmission carry the same information in it as the transmission itself?)

submitted by /u/FoggyDonkey
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