studiot

You clearly don't want to understand since I offered you an alternative treatment using neighbourhoods and you ignored it totally. The beauty of neighbourhoods is that it does not depend upon whether or not there is a smallest real number or a nearest real number or what happens at infinity. And yet neigherbourhood analysis arrives at the same results as the other approaches you have been arguing about.

Happily I prepared this list of tips for someone like you just recently. (W10 is much like W11) I have emphasised the answer to your question in the list but the others may be of use. Windows 11 Create Local account https://support.microsoft.com/en-us/windows/create-a-local-user-or-administrator-account-in-windows-20de74e0-ac7f-3502-a866-32915af2a34d https://pureinfotech.com/create-local-account-windows-11/ Turn off one drive https://support.microsoft.com/en-us/office/turn-off-disable-or-uninstall-onedrive-f32a17ce-3336-40fe-9c38-6efb09f944b0 Create recovery stick https://support.microsoft.com/en-us/windows/create-a-recovery-drive-abb4691b-5324-6d4a-8766-73fab304c246 Save webpages https://support.microsoft.com/en-us/office/save-a-document-as-a-webpage-d1cf1c33-e854-4f9d-bd51-93f94da0f4e3 Skype some versions of w11 come already loaded some you have to get (free) from Msoft. So type 'get skype' into the search box and follow the instructions Recovery Options https://support.microsoft.com/en-us/windows/recovery-options-in-windows-31ce2444-7de3-818c-d626-e3b5a3024da5 https://www.online-tech-tips.com/computer-tips/how-to-boot-to-windows-11-10-system-recovery-options/ Wordpad Type wordpad into the search box at bottom left. This will allow you top open, write and save word docs Initial setup internet bypass https://www.wintips.org/how-to-bypass-internet-requirement-in-windows-11-22h2/

So it is good that you are interested enough to look. However I also said more about them than in your quote of my words. Note I was bringing in your comment on geometry. I was not disagreeing with it. Since I thought you and others might be interested The equations of constitution are the controlling statements or principles, preferably in the form of equations, in physics, chemistry or the science of interest, that are being invoked or brought into play. For example Newtons Laws of motion. Bernoullis's equation in fluid mechanics. The Law of mass action in chemistry. The electrochenical series in chemistry The differential equations of displacement of a loaded beam. Hopefully you get the idea. But these equations are applied to real systems they have no meaning in isolation. And real systems introduce constraints of their own. Many of these constraints are geometric ones, others may be conservation laws. So we often pair the continuity equation (conservation of mass) with Bernoulli conservation of charge with calculations on chemical reactions. Such equations are called the equations of compatibility. But as I said they need not be actual equations for instance we have the beam displacements at the supports must = zero to pair with the beam differential equation for which there are many mathematical solutions, and we must pick a solutions that satisfies the compatibility condition. This particular example is a simplified version of the basis of quantum mechanics, wher we must pick integer solurions to fit some system geometry. Are you beginning to get the idea ?

And ?

You may have crackpot tendencies, we all some in us I suspect, but you do try to reconcile your worries with conventional thinking. Crackpots tend to want to override everyone else. I can offer counterexamples for both of these claims. The Chinese observing and recording the supernova in the Crab Nebula in 1054 were just in the right place at the right time. They were not speculating any observation of the sort. The discovery of penecillin was a pure accident, no cnjecture, bold or otherwise was involved. In relation to your original comment that cause this thread. Have you ever heard of the equations of constitution and compatibility ? This is a very convenient way to divide up the maths. Compatibility is very often represented by some geometrical constraint.

I agree IMHO the 'machinery' is the interaction of physical properties. It should be pointed out and remembered that there are nearly always alternative methods, often using different physical properties to analyse or solve a particular phenomenon. It is very comforting when these different methods arrive at the same outcome. Even more comforting when that common outcome concurs with observation.

We all do it. I find a glass of Laphroaig helps at such moments.

My sincere apologies. I was rushing it. St Petersburg is in the Moscow time zone, which is GMT +3, although as you say it is sufficiently west to be actually 1 hour behind Notice the line in the BBC introduction Perhaps it always has been, I have not been able to determine this but in those days they used 'solar time', but for a whole area so it is reasonable to assume they followed the then capital.

They were well aware of the variation of time (of noon) with longitude by that date. I hour for every 15o longitude. Huygens published the first statement of what we now now as the astronomers and surveyors equation of time in 1665. I made my comments becasue I was suprised at the choice of St Petersburg, especially as it was a late established city and not made capital of Russia until 1712. But we had just fought a war with Russia. Of course the second reference was to the famous story about the international date line, published in 1872. Also at that time as noted there were many 'prime meridians' @Genady It is the meriadians, not the parallels that determine time. https://en.wikipedia.org/wiki/Prime_meridian#List_of_historic_prime_meridians_on_Earth The Russian one at that time was the Pulkova Meridian https://en.wikipedia.org/wiki/Pulkovo_meridian There was also the Paris rival to London https://www.solosophie.com/paris-meridian/

I find it interesting that knowledge of timezones was required in 1859, which was just after the Crimean War and just before the Jules Verne book "around the world in 80 days."

I wonder what temperatures you are working at ? The old DeaconProcess operated at 450oC. Here are some facts and figures about hypo.

Yes I am a musical dunce too, so I had no idea at all. Thanks for the comment on the order. I did find the range of subjects interesting though.

There are 8 questions, click the orange button under the photo in the link to start. I got 7/8 as I didn't know anything about the last one. https://www.bbc.co.uk/bitesize/articles/z8mvhcw?at_mid=n1brDq52Z7&at_medium=display_ad&at_campaign=Victorian_Exam_Paper_Quiz_NewsPromo_PNC&at_ptr_name=bbc&at_campaign_type=owned&at_objective=consumption&at_ptr_type=media&at_link_origin=promo_box&at_format=image&at_link_title=Victorian_Exam_Paper_Quiz_NewsPromo_PNC&at_bbc_team=BBC

Also Nice list Markus, +1. Try this

This notion has already been posted and ignored. However there is more mileage in the reciprocal idea if we perform our analysis in terms of neighbourhoods. We can, for instance introduce the "neighbourhood of infinity". Backtracking and side thoughts apart, there is much to be said for the concept of neighbourhoods, in particular the neighbourhood of infinity as noted above. This helps avoid making ridiculously self contradictory phrases such as "infinite number". Paragraph D from Thurston below takes pains to point out that infinity only behaves as a number in some ways

[math]\frac{{1 - x}}{2}[/math] math]\frac{{1 - x}}{2}[/math [math]\frac{{\left( {1 - x} \right)}}{2}[/math] math]\frac{{\left( {1 - x} \right)}}{2}[/math

As this is outside my experience, I am simply going to add @exchemist , @OldChemE and @sethoflagos who may welll be better placed to help you.

I see that you have just joined SF and offered us a couple of good posts, so welcome. Please note that you can only make a total of 5 posts in your first 24 hours as an anti spam measure. After that you can post at will. Don't you think that your view of Physics is a little narrow ? Much of Physics is concerned with observation and measurement. More is concerned with collating, cataloguing, classifying and correlating theory and observation. And some lines of physical thought are certainly rational but they are not mathematical. Go well in your membership.

This is a strange question, let's look into it further. If you take a helicopter and and hover above the surface - what do you mean ? If you take a helicopter and hover above the helipad for 12 seconds, 12 minutes, 12 hours or 12 days you will still be abov the helipad and not above the other side of the world. If you fly the helicopter so you have some forward or backwards speed we distinguish two speeds Ground speed And air speed The ground speed is of course zero when you are hovering over the helipad. But the airspeed is only zero in 'still air'. Still air means the air is actually turning with the Earth at the same rate as the ground. Otherwise it needs to be enough to counteract the tendency of your craft to move along with the wind and then needs to be some more if you actually want to go anywhere. However the Earth's rotation does play a part since the flying time London to New York is 8 hours, Whilst the flying time New York to London is only 7 hours. Is this actually the phenomenon you are actually thinking of ?

Impressive and patient replies. +1

Thanks that useful. I can expand the explanation in the light of this. Also I added the comment about the old name as it is an example of old use that people still come across in life or literature. For example many still use weight (eg the pharmaceutical industry) not mass, as of course they weigh things to get the mass. They still use W, not M is mass ratios. Also M can be used for the mole ratio, which is also fundamental. There you are then. How much do you know or need to know about concentrations and dilutions ? Yes, although I didn't change the volume formula to suit. So long as you use the same units for all the quantities it doesn't matter. But there is an added twist with volumes as you may need the densities to make the calculations work properly. The mass ratio is the fundamental fraction. You may have noticed that it is easier to use the fact that sum of the % masses of the two substances in the mixture must add to 100% than to use my fraction. It is not necessarily the case that when you add two liquids together the resultant volume is the sum of the individual volumes, the volumes must be corrected to the mass ratio (using the densities) as this is the always true for masses or fore mole counts. In fact at normal temperatures HCl is a gas so will dissolve without much volume increase and you may have pressure as a measure and need to use the gas laws to get to the mass or mole ratio.

OOPs I posted the wrong equation for the mass ratio. [math]\frac{{18}}{{100}} = \frac{{{M_{HCl}}}}{{{M_{HCl}} + {M_w}}}\quad where\;{M_{HCl}} = 18[/math] is correct

Looks like a worthwhile resource and a prime example of that part of science ( all the grunt work of filling in) that doesn't attract the glory. +1

Wishful Thinking seems to be buried deep in the human psyche. Most folks seem to be happy to keep it in its place, so people don't really believe in Santa Claus or Harry Potter. Huge industries, some legal some not and some a bit iffy, are based on this. It seems to be a double edged sword as some of the best of human endeavours and aspirations are the result. But also some of worst and of course the boring inbetween such as science deniers.