studiot

I hope so too. If I didn't think conway had started sprinkling the red dust around, undoing my encouragement for Sato, I would point out to him that case (3) is probably the zero he is looking for.

Hello Strange, I think you have to be careful here as the terminology is confusing. Is the introduction of set theory appropriate because zero is an element of some sets, as well as a set in its own right in some circumstances. It is very easy to become confused between sets, elements, the relationships between sets and the relationships within sets (i.e. between elements) and properties of sets and properties of elements. This is particularly so when the elements themselves are sets in their own right. Here the terminology is not universal. I like Simmons' approach to call sets of sets 'classes' when there is any doubt. Anyway you are not strictly correct to say that zero 'is' a set. Consider the following. Let there be a set of elements. S, denoted {a, b, c , d} etc, equipped with a relation between elements, called multiplication, that produces a member of the set. a * b = a member of the set [math]If\;(a,b) \in S\quad then\quad (a*b) \in S[/math] Three possibilities arise 1) a * b = c where c is different from a or b 2) a * b = a for every a in the set 3) a * b = b for every a in the set Result (2) makes the value of b one: 'b' is then known as the identity element Result (3) makes the value of b zero: 'b' is then known as the zero element But not all sets have an identity element or a zero element or both.

Firstly a small correction The word is spelled pendulum Yes you are right the period of the pendulum is equal to 2pi root (l/g). Note the brackets I have added to make the formula clear and correct. However the acceleration term is not g when there are additional forces involved. Remember acceleration = net force / mass The mass has not changed but the net force has changed due to the additional bouyancy force which acts to reduce the gravitational force (weight) and therefore the acceleration. So the pendulum swings mores slowly under water. Here is a record of a practical experiment and explanation. http://www.millersville.edu/physics/experiments/038/index.php

I was congratulating Sato on his distinction between a set and a space. A set is the more general object. Here is Simmons' version of the statement You should be aware that the words 'set', 'space' and 'relation' have special meaning in Mathematics.

+1 Which affects what parameter in the formula for the period of a pendulum?

First time I've seen that fundamental definition of sets and spaces distinguishing the two, pointed out here at SF. There are some others who could also benefit from noting this. +1

Good morning wtf, and thank you for your contribution. The question in this thread is about the minimum number of properties possessed by an element, not the set properties. In the case of your examples each element has multiple properties. So I am interested in sets where the elements have only one property; I have displayed such a set. Since such a set can be displayed, there cannot be an equivalence relation on this particular set. As regards to your constructed partition of the reals, As I understand it, you have partitioned the reals into two sets: the rationals (you have called set V) and the rest (I am calling W) Consider any [math]a,b \in V[/math] Then [math]\left( {a + b} \right) \in V[/math] Thus a and b have at least two properties.

Those who made too much of units had a point, but went too far IMHO. If your numbers had worked out, your statement could have been made too work with suitable adjustments, Instead of attacking the whole idea. Consider the following (correct) statement. There is always one more post than panel in a fence with no gaps or loose ends. Two different units, but it is possible to compare the numbers.

Your information provides no sense of scale so I cannot follow the connection between iron balls rolling around in chambers and planets and their gravity. You have to consider the time lag between the change in the magnets' field and the ball.

You need to be careful here since your original premise is not even true numerically. Consider the question For what values of r is [math]2\pi r < \pi {r^2}[/math] ? Set [math]2\pi r = \pi {r^2}[/math] then [math]{r^2} - 2r = 0[/math] [math]r\left( {r - 2} \right) = 0[/math] r =0 or r = 2 For r<2 the statement is numerically incorrect anyway. It is easy to see and test by substituting r=1 that the perimeter is going to be numerically greater than the area since 2 > 1.

OK so do you understand what the first equation you posted means and where it come from? I ask because in your project instructions they tell you where it comes from immediately before they quote it. Why are do they have you measuring the voltage across a resistor? What does that tell you?

Even if there is an odd number of magnets? With all the changing of field, I am not sure if a linear array would produce a strange attractor, I would expect there to be a chaotic frequency doubling at some frequencies of operation.

My thoughts are that you are overthinking this, when you should be listening harder to what others are telling you (that is the easy way) Merry Christmas.

So what about a statement of the problem to include all the facts? Followed by your revised solution? All the facts include the assumption both imatfaal and I made that the vertical acceleration is upwards. This is important since the answer is different if it is downwards. You have been told that both gravity and the vertical acceleration play a part in this so over to you?

I am not sure what point your musing is trying to make, but how does about latent heat and phase changes fit in? Do you not supply exactly the same heat to melt something as you get back when it refreezes? Fourier's Law is about energy (heat) transfer. The First and Second Laws are about energy interconversion.

Without gravity the words horizontal and vertical have no meaning.

Interesting way to put it, but yes the liquid is at all times subject to the third acceleration.

Some of the links on the first google search page were dated 2007, which I agree I stretched to a decade ago.

You might find the following interesting reading. Lomborg The Skeptical Environmentalist.

The above was created by selecting the quotation bubble (13th tool from the left) on the second line of the toolbars. Then copy and pasting the excerpt from your post Then identifying the author of the quote as yourself by typing in your name. In response to your question about potential energy Yes you are wrong. Any energy a body possesses by virtue of its motion is Kinetic energy. Any body of the same mass and charge at the same position would have the same potential energy, regardless of the velocity of that body or even if it was no moving at all. If it's velocity changes as a result of a position change this kinetic energy changes any change in its potential energy is totally independent of its kinetic energy or changes in its velocity. So a body can circle at a constant radius, speed up or slow down whilst circling and its kinetic energy will change, but its potential energy does not change. Conversely a body can change its radius so cahnging its potential energy and simultaneously maintain its velocity so keeping its kinetic energy constant. There are further energy considerations for these events to occur since work has to happen to cause them.

Even if we allow that either 1) The OP hasn't read the question properly and it actually reads or 2) The question was badly posed and it should have read "partly filled" I would have expected some greater understanding of the question by the OP. There are three accelerations to consider in total, not two. When you consider all three the quoted figure is incorrect I make the slope tan-1(1). Samagra, do you understand either the mathematics or the physics of what is going on? The problem can be solved as an exercise in applied mathematics or and exercise in physical understanding and physical reasoning. DimaMazin, instead of butting heads with swansont, you are nearly there on the physical reasoning approach tidy up your work and complete the job. The subject under discussion is known as relative equilibrium of liquids; googling this will reveal many learned articles and sample calculations for many circumstances.

I have a feeling that Mike is putting forward the Fresnel Principle Natura simplex et fecunda http://www.if.pwr.wroc.pl/~optappl/article.php?lp=637 To which I would offer G N Whitehead's reply Seek simplicity and distrust it. I must congratulate Mike for inventing a new method of proof. Proof by overwhelming numbers of pictures. How I wish that many posters of questions here would deign to draw only one. My favourite phrase seems to be Draw a diagram.

This seems like homework/coursework. Since it is a project we don't do it for you but can help you by commenting on ideas you present to us before you have to present them to your mentors for marking. You have made a good start so here are first comments. What part of the project are you going to design yourself and what part are you going to use off the shelf modules for? A block diagram would be very useful. There are several considerations to take into account at an early stage when designing something. What are the power requirements and what will be the power source? You can obtain ready made modules for your signal generator, but willthey supply enough power by them selves or need boosting? Details of the actuation needed are required to determine the actuator. Are you going to consider the mechanical requirments to absorb the thrust from the workings of the actuator? So the overall project can be broken down into functional blocks, each of which has its own power and weight (and perhaps cost) budgets and also specific input outputs and special requirements.

Asking where did the energyof the atoms and molecules come from in the first place is like asking where did the atoms and molecules themselves come from. We don't know, but if we did you would only be asking where did whatever spawned them come from and so on for ever.

Kramer, There are tools in this forum to help lay out your answer so others can more easily see what was said by someone else and what was the reply. Using those tools to look at the comments and replies we can more readily see that you are mistaken in your assumptions. Motion is not connected with Potential Energy in any way. As regards your response to me Do you think the tax man would let you off filling in the last 53 boxes on the tax form just because you wanted it simplified? C'mon Lagrange 1736 to 1813, Hamilton 1803 to 1865 so the mathematics is hardly modern. As to its relative level I don't know what maths you know so I can't comment, but you can understand it with an old fashioned British A level in maths.