In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.
In some textbooks and popularizations, the empty set is referred to as the "null set". However, null set is a distinct notion within the context of measure theory, in which it describes a set of measure zero (which is not necessarily empty). The empty set may also be called the void set.
I take the origin to be at the apex of the cone. Using the similarity of the triangle, where ##r## is radius of water and ##y## is height of water from the apex of cone:
$$\frac{r}{y}=\frac{4}{10}$$
$$r=\frac{2}{5}y$$
The mass of water = ##\rho .V## = ##\rho . \pi r^2~\Delta y## = ##\rho . \pi...
Does electron beam in empty space generate magnetic fields around them just as with current in conductor.
If yes, then is it experimentally proven that two parallel electron beam would attract each other.
With the cost of living crisis. my fridge has a bottle of milk in it by itself most of the time. Would it cost less in energy if i fill the fridge with bottles of water to fill the gaps? hope this makes sense.
Calculation of the potential electrical energy generation of a siphon pipe, emptying an enclosed reservoir and end of siphon pipe connected to a pelton turbine with efficiency of 75%
Known inputs:
Height difference of siphon(Hd) = 4,5m
Height lift of Siphon (Hu) = 6m
Total siphon pipe length...
a tank is filled with water up to its brim a hole was made at the bottom of tank find time taken to empty tank if water flows at rate of 2h kg/s where h is height of liquid column and is equal to 20m radius is equal to h/2
[Moderator's note: moved from a technical forum.]
Hello, there. From another post, I read the insights Learn the Physics of Virtual Particles in Quantum Mechanics and Explore The Vacuum Fluctuation Myth in Quantum Theory.
Also, I sometimes see a statement that the vacuum is not empty from some media. Most often, it says the vacuum can create...
Inserting wires in existing empty conduit
There is an empty PVC conduit size 1.5748" (40mm) in the main entrance panel. It was built around 8 years ago. There is metal wire (see picture above) inside the conduit to pull the main electrical wires from the inside or outside. Is there any...
So, another poster triggered this question in my mind when saying old urine can smell like ammonia.
If this is TMI (talking about urine), please feel free to tune out of this thread. :-p
For those sticking around, I use a pee bottle at times on the road (this was even pre-COVID, before...
For instance, I attached two problems in the the thumbnail below. I’m curious why A cannot be the empty set in 18b, but A is not excluded from being the empty set in 17a.
In 17a, if A is empty, then all the hypothesis can be satisfied (the composition will be empty too, obviously), but g need...
In a closed circuit the battery sets up a potential difference which causes charge to flow. I understand potential difference as the
measure of electric potential energy per unit charge, the amount of energy required to move a charge from one point to another per charge.
for example when a...
In an elementary school version of set theory, we can take the complement of the empty set to obtain ##\emptyset ^ C = \mathbb{U}## However, in a sophisticated version of set theory, the concept of a "universal set" ##\mathbb{U}## is problematical. ( So says the current Wikipedia article on...
So I know it's generally not a good idea, but I wondered what actually is the limiting factor. Does the magnetron heat up much more quickly? - and if so what's the physics going on that's causing it to heat up - is it increased current in the resonant cavities ? Also is it bad for the cathode...
The intention of this question is to get to the heart of the geometrical properties of space-time according to GR, and to focus entirely on what the theory allows, and not so much on what we actually see. I would like to consider a perfect vacuum, in a euclidian infinite void, completely devoid...
Its stated that empty universe should have a hyperbolic geometry (Milne Universe) but I don't understand how its possible.
$$H^2=\frac {8\pi G\epsilon} {3c^2}-\frac {\kappa c^2} {R^2a^2(t)}$$For an empty universe when we set ##\epsilon=0## we get
$$H^2=\frac {-\kappa c^2} {a^2(t)}$$...
I am not sure this question has been asked here before but I am curious about it. From the Modern Physics Course, I learned that we need a nucleus to create an electron and positron pair (with a photon). And the reason is stated as to conserve linear momentum. If this is the case then how the...
Trying to learn the game Go. I have a question in regards to the uploaded pic. Why is the empty spot neutral? Couldnt white just place a stone there and capture all of the black stones since all of blacks liberties would be taken?
Homework Statement
We want to fill a bottle with R-134a. The fluid comes from a fluid line.
The bottle is initially empty, the bottle volume is 12 litres, the bottle is insulated (adiabatic filling).
The fluid line contains R-134a at 20 bar, saturated steam.
Homework Equations
Using the...
Hi all, I am having trouble understanding the some ideas presented in some notes I've been reading, help is greatly appreciated!
I've uploaded screenshots of the material I'm referring to below, the last two images are what I'm mainly referencing, and the first few are to provide context...
The main aim of my question is to find time taken by gas filled tank while emptying (from full to zero) it into atmosphere?
I require a set of equations which might be used in the calculation of such a situation.
Known parameters are:
1. Pressure inside the gas tank.
2. Dimension and shape of...
If a black hole that is feeding is actually ingesting the spacetime around it (and hence whatever may lie in that spacetime including light) what does it do when it is not ingesting but nonetheless has very strong gravitational attraction?
Does it sit there dragging empty spacetime into it? If...
Homework Statement
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I'm not a native english speaker, so I apologize if my explanations are a bit awkward. I do not have a solution to this problem and I'd be grateful if someone could check this/help. I also have absolutely no idea how to even begin. Asked my colleagues, none of them know...
I having difficulty wrapping my head around a concept that I wish to solve. I have a 10L tank of compressed air at 100psi. When an outlet hole of cross-sectional area of 0.115 in^2 is opened, I wish to develop a curve of pressure vs. time from t=0 until pressure drops to atmospheric. Many things...
Homework Statement
Let ##J = \emptyset## and ##A## be any set. Then ##J \subseteq A##.
Homework EquationsThe Attempt at a Solution
Proof: Suppose that it is false that ##J \subseteq A##. Then ##\exists x (x \in J ~~\text{and}~~ x \not \in A)## is true. But this is a contradiction, since...
A question arose over a simplification I wrote on another subject. My i information say's that matters antimatter pairs are generated in what is known to be very empty space such as the voids within the cosmic web. When I read about this it was considered anomalous but definitely verified.
Now...
Homework Statement
problem 23:
A large tank is filled to capacity with 500 gallons of pure water. Brine containing 2 lbs of salt per gallon is pumped into the tank at a rate of 5 gal/min. The well mixed solution is pumped out at the same rate. Find the number A(t) of lbs of salt in the tank at...
Do you know where I can find a formula to calculate how long it would take to drain a cylinder under pressure to atmospheric pressure? if I know the volume of the cylinder and the size of the opening.
I was recently tutoring a first year student, and a question of her assignment was as follows:
Suppose that that you have a bucket of water over a scale. If you then partially submerge an iron rod in the water, while holding the rod so that it does not touches the bucket, will the reading on...
So, here's my question. I read somewhere that all universal truths on empty domains are vacuously true, whereas all existential are false. However, if all statements of the form (∀x∈A)(P(x)) , where A is an empty set, are vacuously true, then the statement (∃x∈A)(P(x)) should also be true...
Hey! :o
Let $V$ be a $\mathbb{R}$-subspace with basis $B=\{v_1 ,v_2, \ldots , v_n\}$ and $\overline{v}\in V$, $\overline{v}\neq 0$.
I have shown that if we exchange $\overline{v}$ with an element $v_i\in B$ we get again a basis.
How can we show, using this fact, that the intersection of all...
I need a clear-cut explanation of vacuous truth, as I can't seem to wrap my head around it. I guess this more precisely comes down to why we organize the truth table for the conditional statement the way that we do. Also, in connection to this, I'm wondering why the empty set is a subset of all...
Can someone explain to me why there must be a real/meaningful space inside of a black hole?
I have been autodidactically working on understanding the mathematical concepts that general relativity is based on, so I've never had anyone to ask questions to (until it occurred to me to find a forum...
I have a problem understanding where does the matter/radiation go to because of the expansion of our universe. Eventually all normal matter and radiation will leave our causal patch, but the word leave is pretty unconvincing in this case.
They will stay in their own causal horizon until each...
Hello everyone!
I would like to ask you if anyone can help me solving my Problem with mcnpx. I created a file with a watertank, a nozzle and a slit blend on the surface. I also inserted a protonbeam and would like to plot the dose and fluence for examplte with Moritz. But when I execute the...
Our Professor said there will be still an electric field in empty space even without charges.Hows that possible.Space-time has a some quantum property that acts like this ?
I'm a computer science student. I'm currently learning electronics so that I can program embedded devices effectively. I'm reading from the free book at allaboutcircuits.com.
Why is the voltage between two points on a wire in a closed circuit equal to zero? Note that between these two points...
https://www.sciencedaily.com/releases/2016/11/161130082804.htm
Is there any other detection's to back this up?By studying the light emitted from an extraordinarily dense and strongly magnetized neutron star, astronomers may have found the first observational indications of a strange quantum...
Hello,
I am in my first class for C++, so I apologize in advance if this question is amateurish. To be clear, this project is already finished, and what I am trying to do already counted points off against me; I am not interested in cheating, I just want to know what the answer to my issue is...
Hi everyone,
Recently I randomly thought of a thought experiment of something going faster than light, along the lines of a shadow or some other "non-information carrying object". In this case it would be an empty seat.
The idea is to take 800 million and one chairs of half a meter breadth...
The empty set has a cardinality of 0, yet it is found in all sets and as we know any sets within a set are counted as a single element. But it never counted as an element in the cardinality of a set?
For example: The set {1,2,3} contains 8 distinct subsets including the empty set, as taken by...
I know what a proper subset is, but I never understood why every set has the empty set as its subset?
I mean, is the reasoning something primitive like this: if I have x objects, the number of unordered sets of elements I can make are 2^x, including the case where I throw out x objects and...
1. A goblet consists of a uniform thin hemispherical cup of radius r, a circular base of the same material thickness and radius as the cup, and an intervening stem of length r and whose weight one quarter of that of the cup.
(a) Show that the height of the centre of gravity above the base is...
Homework Statement
This is Exercise 15.2 in MTW - See attachment
Homework Equations
See attachment
The Attempt at a Solution
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My attempt at a solution is also in the attachment.
Are my initial assumptions OK? If not can someone nudge me in the right direction.
If my initial...
Please post scientific analysys like measurements.
I want to see what they measured with measuring devices.
I tried searching Google. Couldn't find any good paper on the subject. Only answers that it's empty and that it's not empty.
Always contradictions when searching on Google!
If I have a 1 km cube of empty space at a constant temperature of 2.7 K, how much energy do I have? That is, if I know the total volume of space in the universe and I know what the average temperature of that space is, can I computer to total energy of the universe?
An ellipse has two foci. For a planet in such an orbit, the star is at one of the foci. The other is empty.
According to Ptolemy, if we draw a line connecting the planet and the empty focus, we will find that the line moves at a constant angular velocity.
Is this true, or is it a crude...
I am kind of wondering how much for example CO2 you would put out or other greenhouse gases would be emitted everytime i use a full tank of gas. It would help me if you could explain it in volume, like how much it would take to contain the emissions on its own, and how much it would take to...