Carrock

This may be a little misleading. Classical physics does not claim that increasing volume violates energy conservation, as you seem to imply. Assume a sealed container of gas. When you slowly expand the container the gas does work on the container walls. Its temperature goes down because some energy has been removed from the gas in the form of work etc. Energy has not been destroyed. Classically if you release some gas into vacuum, the gas is not in equilibrium and the volume containing all the gas increases indefinitely. The total energy of the gas does not decrease as the volume increases. Black body radiation refers to radiation from a body in thermal equilibrium. As the CMBR is not in thermal equilibrium in the sense required for equilibrium thermodynamics to be valid (which it has not been at least since ~400,000 years after the B.B.), the stretching of wavelength is due to the spatial expansion of the universe and nothing to do with near equilibrium thermodynamics. Indeed this creation of space and wavelength stretching is in violation of classical physics. As it happens, the stretched CMBR has the same spectrum as radiation from a 2.7K black body, with a few imperfections. This is pretty consistent with the CMBR being radiation from a black body at 2.7k but there is a massive amount of evidence inconsistent with this view. It might be less confusing to think of the CMBR having a colour temperature of 2.7K much like a cool running LED lamp might be described as having a colour temperature of 3,000K. ie colour temperature is a description of a spectrum, not the temperature of the source.

You clearly regard a gun's potential to kill the people it's aimed at as the primary, perhaps only, measure of its safety. I'd agree to an extent. However, the widespread view that guns improve personal safety, the general absence of a requirement for competence and the idea that safety is measured by the ability to shoot the intended target are mitigating circumstances. There is no requirement, in general, for competence in a gun owner, so in many cases even a 'safe' gun will kill apparently innocent bystanders rather than suspects. The number of shots that can be fired is important, since the more shots, the better the chance of killing the suspect. A perfect crime if you're careful and a bit lucky: I've seen a few 'true crime' stories where a spouse kills several partners 'accidentally' before the police get suspicious enough to look for evidence of murder. Even then, abysmal stupidity by the perp or dubious evidence is often required for a conviction. The most powerful, lethal gun (with a light trigger action and easily disabled safety catch) is therefor the 'safest'.

More dangerous for the user certainly. Even the most law abiding citizen is potentially dangerous and may get you in legal trouble after you fail to kill him/her with an inadequately lethal gun, even if you honestly believed (s)he was intending to attempt to kill you.

Because the earth wobbles ie precesses, Polaris will not be the pole star indefinitely. From https://en.wikipedia.org/wiki/Thuban

Exponential spatial expansion forever is not compatible with known or AFAIK speculative physics. There would be [latex]{2}^{\aleph_{0}}[/latex] finite units of space ie as many finite units as there are zero volume points in the universe, which is generally considered impossible. This issue can be avoided by saying that that at indefinitely distant past and future times the universe is not expanding, but you still have to explain why expansion started and eventually stopped.

But you would be wrong within currently understood physics, so that would be a bad idea. Seems I was wrong about the meaning of .

You could also say that you and the ball are stationary and the ball is pulled outwards by gravitational force caused by the relativistic effects of the universe rotating around you.

This maths is rather beyond me, which is why I stopped posting in these topics. However, from http://web.mat.bham.ac.uk/R.W.Kaye/seqser/density.html and some other pages, I couldn't find any any indication that the set of integers is not dense in the same sense that the rational numbers is dense. e.g.

Small correction maybe. Surely the rationals must be discrete or they'd be uncountable and could not be mapped to the integers.

No, but I said moved, which your latest post indicates is impossible, not removed. Overvoltage can destroy resistors though I'd not expect it if the 110V rail is always between 70 and 150V (which I suspect it isn't). C8 ensures that most of the A.C. voltage transients appear across R25/R26. C8 isn't needed to protect the inverter but it may be needed for reasons you know about but I don't. Based on the limited information you've provided I'd suggest: Remove C8 and replace R25/R26 with either one 110 ohm 1 watt resistor ( for its higher voltage rating) or with two one watt 220 ohm resistors in parallel. There are many possible reasons this won't work but I'm done with guesswork and this topic. I hope this helped.

A few points. If the converter is switch mode I doubt there's significant equivalent input capacitance. Is the dc input fairly constant? eg rectifier+capacitor? (But rectifier+capacitor drifts up to peak input voltage - 150V - if there's no load eg prior to closing DC power switch.) If so C8 isn't needed or can be replaced by a smaller value. It's probably taking nearly all the surge current rather than the 110Vdc to 24Vdc converter. It may then be better to switch the power source for the 110V D.C. input if that is possible rather than the D.C. output. If the input is rectified unfiltered A.C. C8,R25 and R26 should be moved. I think that would be a safe approximation.

This could be good, depending what you want to use the pulse duration length for. I suspect your application has many similar solutions by other people and you could adapt your circuit in that light. eg is it really necessary to deliver 0.76J at 50Watts?

You're relying on the non repetitive surge rating of the resistor, which is a function of peak power and energy of the surge. You may also be exceeding the smaller resistor's voltage rating. These things depend on the resistor design; you'd need the manufactuter's data. The whole resistor doesn't have to warm up for the resistive part to burn out; a fuse burnt out by a surge typically remains cold while it may be warm if it blows through a continuous slight overload. If you're using a 10W wire wound resistor I'd expect the thermal inertia of the wire to cope with a 3 1/2 joule 50W peak pulse. Otherwise, without more information the only reliable solution is a 50W resistor. [edit] maybe 25W if two resistors[/edit]

Yes. When n→∞, it has to start from 1, then +1 then +1 ...... At each step, n is a finite number. In fact, n is not kept finite, but cannot be infinite, that is, never n=aleph_0. So, real number cannot be mirrored by digital numbers. I will try another approach. I assume you accept that there are [latex]{\aleph_{0}}[/latex] elements in the infinite integer series 1,2,3..... ie the series does not end at some arbitrarily large finite number. If not, I'm done. Rather than count n by starting from 1, avoid that objection by simply constructing figure 3 in the same way as you construct the infinite integer series, with each distinct n set equal to a distinct positive integer. You don't have to count or iterate or step through every or any value of n; constructing either the infinite integer series or figure 3 does not require you to 'count' every member. If you consider the number of rows generated by different values of n to be finite, you have to explain how n cannot be set equal to some members of the infinite integer series 1,2,3..... If this proof I've outlined here and earlier in thread, that there are [latex]{2}^{\aleph_{0}}[/latex] ie [latex]{\aleph_{1}}[/latex] distinct binary fractions is valid, your contradicting proofs must be invalid.

Bertrand Russell opposed this view saying, (approximately) that such a series can be defined and used. There's a good discussion of this issue, which I won't/can't attempt to argue, on page 29 of Philosophy of Science Vol. 32, No. 1 (Jan., 1965). (free registration on site required to read it) Even if you don't accept this, I think there is another flaw. If n can't ever reach aleph-null, then you similarly can't ever reach even an (aleph-null)th member of the above counts ie you can only make an unbounded finite count. If you argue that you can calculate what the result would be if you could count up to aleph-null, then are you not accepting you can similarly calculate the result of n reaching aleph-null?

In "2" you say "Because the intervals are always empty when n→∞, the set of all fractional binary numbers is not continuous but discrete" I suspect you implicitly mean by n→∞ that n is or becomes larger than any given finite number but n is still finite. You then have 2^n +1 discrete points which maps to a subset of the rational numbers. Only if n=aleph-null are all the real numbers (from 0 to 1) represented and there are are then no intervals between numbers. I agree that "binary numbers has the same cardinality as the real numbers" but by keeping n finite you are only listing a countable, finite set. You can create an aleph-null set of real binary numbers by mapping to eg an infinite set of integers. You can create from that set an aleph-one set using Cantor's diagonal method. I think all real numbers can expressed as a binary or decimal mixed number or mapped to a finite range of values eg 0 to 1. pi eg can be expressed in decimal or binary but it's not a countable number. tnx pengkuan: this was a useful learning experience for me and I hope you.

I was just pointing out specific errors. I looked at your second link and while it appeared to be accurate, I think it's pretty well impossible to use it for learning. You might find this refutation, using transfinite maths, of the possibility of an eternal expanding universe Philosophy of Science Vol. 32, No. 1 (Jan., 1965), pp. 21-31 interesting. (free registration on site required to read it) It's very clearly written as many people resist transfinite maths' concepts. One 'expert' here knew its conclusions were wrong without even reading the abstract.

An infinite quantity of pure gold contains no silver. There is an infinite range of frequencies in the visible light spectrum; the number of colours is a lot less (or more) than 16,000,000 as colour is subjective and eyes cannot distinguish that many. Main problem: where on the canvas is the picture of the entire canvas?

I suspect most professional hackers no longer support XP hacks. Free antivirus seems entirely adequate to block attacks. As there is around a ten minute window between Microsoft removing enough bugs for an OS to be usable and ending support for the OS I only upgrade when I have to. I have tried 10 or 11 on a friend's rarely used computer for software whose main enhancement is XP incompatibility. I enjoy a leisurely toast and coffee while it's booting and installing upgrades and rebooting and giving and sometimes cancelling security warnings.

A quote from http://sharpagain.org/how-a-doctor-reversed-her-husbands-alzheimers-disease-in-37-days:

According to NASA, this one is genuine.

My 'problem' with you is the usual one - you expect people to have faith in you. You not only claim not to have used the term 'negative vacuum,' you quote 'negative vacuum' again in your next post. You could not make it clearer that you expect uncritical faith that you are right. Clearly moderator swansont has faith in you and I am probably outnumbered, which is a sad way to end a discussion on a forum with 'science' in the title. As you ignore any criticism you can't refute, this is my last post.

In this thread 'Mordred said 'You can however have negative vacuum' and corrected it to 'A vacuum is a pressure terminology' I don't believe you can usefully define vacuum as equal to one of its propertties. In his OP he said in effect that vaccuum is a number. That was his '1=2 thefor...' moment. If Mordred had read about eg negative gauge pressure and then said 'negative vacuum' and then in a later post confirmed (approx) that vacuum is sYnonymous with pressure I would describe that as a new definition probably created by Mordred's failure to understand the relevant science. I know (just) enough about vacuum energy to know when I'm reading rubbish; all Mordred's OP does is provide misinformation.

I was hoping for a clarification, not an explanation of how you are ascribing an unhelpful new definition to an old term. A few points to consider before reusing your new definitions in public: Air pressure as generally understood seems to fit quite well your definition of vacuum. Must all future measurements of air pressure (sorry pressure terminology) include its expansion/contraction rate or will you define air pressure as a new sort of pressure terminology? As vacuum has been preempted, will the volume aspect of space in future be defined as 'space is a volume terminology'? And so on.... I know you regard science on this site which has not been published in a journal or similar as suitable only for the the trash can but perhaps you have been so busy searching out such posts that you have not had time to apply similar standards to yourself. I usually stop reading your posts when I come across the equivalent of '1=2 therefor...' but on this occasion perhaps you deserve the sort of help you give many other people.