What is Empty: Definition and 271 Discussions

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.

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  1. N

    Exploring the Empty Space of Atoms: The Zero-Dimensional Particle Theory

    If all fundamental particles are zero dimensional, are atoms empty space? And they are zero dimensional, does that mean that we don't exist?
  2. ElegantSir

    Fill in the empty columns of a work/power table

    Homework Statement "Fill in the empty columns of the following table" Table is in the thumbnail Homework Equations work = force / distance power = work / time Y = E * c -Y is the yearly running cost -E is the EnerGuide energy rating per year -c is the cost of electricity per kW/h The...
  3. 24forChromium

    Excel: Entering empty cells with function

    How can I set up a function with an if command such that it only copies values greater than zero from another column while leave the rest of the cells empty (not zero)?
  4. P

    Does empty space have a mass effect?

    I red about that because of quantum mechanics space cannot be empty. Particles and their anti particles pop into existence, and the next moment they annihilate each other and vanish out of existence. But most particles are not mass less, so this noise of short lived virtual particles; i think...
  5. M

    How long will it take for a gas tank to empty?

    Hello all, I have an oxygen tank that is 10 L in volume, pressurized at 500 barr (pressure can be adjusted down to 1 barr out of the tube), and I want to 'bubble' the oxygen into a beaker of water. I will simply use a tube (diameter is around 0.5 cm) connected from the tank and with the other...
  6. Steve Crow

    What's wrong with a flat, empty, and expanding universe?

    I'm new to this impressive forum and have a question that may have been addressed a thousand times, but here goes. A FLRW metric is happy with a time-varying scale factor a(t) and zero curvature parameter k and could care less about density. The combination of a FLRW metric and the Einstein...
  7. S

    How big is an object in empty space?

    Hello, I'd like to share with you a core idea of simple thought experiment which I have had on my mind for a while. I'll be happy if you tell me your opinion and what I am missing. Please note, as English is not my first language, the text below may not be written in the best way (I hope you'll...
  8. skepticwulf

    Empty space in atoms vs orbits

    We often read that atoms are mostly empty space. A common example is given as, if the atom was a big as a football stadium the nucleus would be as big as a tennis ball on the center and nearest electrons circling around at far side of seats or something like that. How does this reconcile with...
  9. S

    Infimum and supremum of empty set

    Hello, I can't wrap my mind around this: inf∅= ∞ sup∅= - ∞ Thank you in advance.
  10. carllacan

    Difference between conductors and empty space

    Inside a conductor, as opposed to inside an insulator, charges are free to move around and reposition themselves, which causes that, if we wait a long enough time, the electric field inside them will be zero. But in an empty space there's nothing (by definition) that can stop charges from...
  11. AL-Hassan Naser

    Free electron or empty lattice schrodinger equation solution

    in the solution for free electron we start with X(x) = A exp (ikx) + B exp (-ikx) then using boundary conditions we eliminate B if the wave is traveling in the positive direction and vice versa my questions are: 1. what is the boundary condition used? 2. is it X(-inf) = 0? because this would...
  12. xwolfhunter

    Question about empty sets in set theory

    So I'm reading Naive Set Theory by Paul Halmos. He asks: His response is that no ##x## fails to meet the requirements, thus, all ##x##es do. He reasons that if it is not true for a given ##x## that ##x \in X~ \mathrm{for ~ every} ~X~ \mathrm{in} ~ \phi##, then there must exist an ##X## in...
  13. Pull and Twist

    MHB Work required to empty water out of a vertical ellipsoid tank.

    This is another problem I am having difficulty with... I set it up like I've been working the book problems, especially the sphere problems, but can't seem to get the right answer. I feel that I am calculating the radius incorrectly. I know I am supposed to us {x}^{2}+{y}^{2}={r}^{2} and r=1...
  14. Paul Shredder

    Structure of a Matrix With Empty Null Space

    Hi guys, I hope you are having a great day, this is Paul and, as you have seen in the title, that's what I'm looking for, let me explain: When you have a square matrix with empty null space, that is, the only solution to the equation Ax=0 (with dim(A)=n x n) is the vector x=0n x 1, means that...
  15. Charles Stark

    A proof the Empty Set is unique

    Homework Statement The problem is to prove that there is only one empty set. Let A and B be empty sets, A is a subset of B and B is a subset of A (by the definition that the empty set is a subset of every set) So A=B (by definition) By convention, all empty sets are equal. Therefore, there...
  16. S

    What would happen if you let a full battery charge an empty

    Suppose you have a full battery and an empty one, both the same type, and you hook up positive to positive and negative to negative, and for this particular battery chemistry, the difference in voltage is great enough to commence charging of the negative one. How much current would likely travel...
  17. 1

    The exclusion of empty substructures

    So, subspaces of vector spaces, and subgroups of groups, are not allowed to be empty. This is because "there exists an identity element". We could include the empty set in these substructures but have the definition otherwise unchanged. I'm curious as to what the consequences of such would be...
  18. Q

    Could the mass of a singularity be described as an empty set

    Could the mass of a singularity be described or defined as an empty set, or else what is the term to describe it (in at least one sentence).
  19. D

    Could the Twin Paradox in GR be Generalized to Completely Empty Space?

    Whenever the twin paradox in GR seems to be discussed, it always seems to be done in the presence of a large mass such that the twins can be considered as test particles moving in some metric. I was wondering whether the same problem could be generalised and be proposed in completely empty...
  20. Stoney Pete

    Salmon's 'proof' for the existence of the empty set

    Hi guys, I stumbled upon this lovely quote from the philosopher of science Wesley Salmon: "The fool hath said in his heart that there is no null set. But if that were so, then the set of all such sets would be empty, and hence, it would be the null set. Q.E.D." (in Martin Gardner, Mathematical...
  21. K

    Empty Box with Plumb Bob Sliding Down a Plane

    Homework Statement You hang a plumb bob inside an empty box. The empty box slides down a friction-less inclined plane. The inclined plane makes an angle of 30 degrees with the horizontal. What is the angle the plumb bob makes with the vertical during the slide? Homework Equations g pulled down...
  22. J

    Do Empty spaces/text slow down code?

    If you are say running a for-loop with 5000 cycles, will 2 empty spaces and say 3-comments slow this operation down?
  23. Stoney Pete

    Empty set disjoint with itself paradoxical?

    Hi guys, I've got a philosophical question for you concerning the empty set. I know that in axiomatized set theory the empty set is disjoint with itself. Because it has no members, the empty set cannot have any members in common with itself. This is common sense in set theory. But if we say...
  24. M

    MHB The rectangle has an empty interior

    Hey! :o Show that the measure of a rectangle is zero if and only if it has an empty interior. When a rectangle has an empty interior, does this mean that the length of the sides of the rectangle are equal to zero?? (Wondering)
  25. evinda

    MHB Proving A is the Empty Set: Exploring Set Subsets and Implications

    Hello! (Wave) I want to show that $A \subset \varnothing \rightarrow A=\varnothing$. That's what I thought: $$A \subset \varnothing \text{ means that :}$$ $$\forall x (x \in A \rightarrow x \in \varnothing)$$ Since, there is no $x$, such that $x \in \varnothing$, there is no $x$, such that...
  26. D

    Why don't these open set axioms specify that the empty set is open?

    In all the topology textbooks I used in school, the open set axoims specified 4 conditions on a set S: (i) S is open (ii) empty set is open (iii) arbitrary union of open sets is open (iv) finite intersection of open sets is openI noticed on proofwiki, that (ii) is omitted. I was curious if...
  27. I

    Empty Space: Energy, Warping, Bending, & Gravity

    If we were to take a region of space which had nothing in it, no particles, no light, just empty space, would this space contain energy of some sort? Also if space can warp, change, bend etc then can space be made of something? Like a material? If empty space is nothing then how can it bend or...
  28. S

    Exploring Matter: Empty Space & Energy

    Learing about matter and what it is composed of, I'm spending a lot of time trying to wrap my brain around the idea that most of our mass is empty space, that the mass of our atoms is calculated and expressed in energy. How is this possible? Are the recreations moving so fast they almost create...
  29. C

    Archived Filling an Empty Tank: Calculating Pressure & Temp

    Hi, A cylindrical object is reentering at a Mach number of say 25 at an altitude of 80 km. I like to calculate static pressure and static temperature inside the cylinder. Yes Obvious, normal shock will form. But the problem is a small orifice (say 20 cm ) is available in the cylinder, the...
  30. X

    An empty ball in arbitrary metric space

    Is it possible for a ball(with nonzero radius) to be empty in an arbitrary metric space?
  31. L

    Dark matter fills 'empty' space

    There is now evidence dark matter fills what would otherwise be considered to be empty space. 'Cosmologists at Penn Weigh Cosmic Filaments and Voids' http://www.upenn.edu/pennnews/news/cosmologists-penn-weigh-cosmic-filaments-and-voids "Dark matter ... permeate[s] all the way to the...
  32. S

    Is empty set part of every set?

    is empty set part of every set?? you have a power set of s represented by p(s) and s is { x is integer and either x=<-2 or x>=5} and you have another set d = {{-3 -2 1}, {4}, {6, 7}, {-5, 6, 9}} when you are asked for intersection of p(s) and d in a plain maths question am I...
  33. MarkFL

    MHB Calculating Work to Empty a Trapezoidal Trough: Jessica's Question

    Here is the question: I have posted a link there to this thread so the OP can see my work.
  34. S

    Empty Boxes Invariant/Algorithmic Problem

    I've been trying to figure this out for a couple of hours and I just don't know how to work it out, I have attempted to create a valid statement for the algorithm, but I just don't know what I'm doing. I would be greatly appreciative for any help I could get on this. Thanks! Homework...
  35. I

    Empty elevator with a max speed going down, find tension on cable.

    My apologies for asking two questions in a short period of time, this is the last question I have. Hopefully one day I'll be skilled enough to answer everyone elses! :) Homework Statement An empty elevator has a mass of 722 kg. It moves between floors at a maximum speed of 6.00 m/s. The...
  36. MarkFL

    MHB Domenic's question at Yahoo Answers regarding computing the work to empty a tank

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  37. C

    Can Empty Space Curve? FRW Cosmology Equations Explored

    If I start with the standard FRW cosmology equations, $${\eqalign{ 3\dot a^2/a^2&=8\pi\rho-3k/a^2\cr 3\ddot a/a&=-4\pi\left(\rho+3P\right),}}$$ and set [/tex]\rho=P=0[/itex] (or $T^{\mu\nu}=0$), I have $${\eqalign{ 3\dot a^2/a^2&=-3k/a^2\cr 3\ddot a/a&=0.}}$$ The second equation gives $$\ddot...
  38. V

    Exploring the Concept of Empty Space: Fact or Fiction?

    Is there in reality empty space where there is no energy or matter? or has anyone seen or detected it?
  39. anubodh

    Exploring the Possibility of Friction in Empty Space Due to Quantum Fluctuations

    Since there are quantum fluctuations popping in and out of existence then there should be an friction in the space though negligible(i know that they disappear in less than planks time but even then there should be a frictional force all round the universe)
  40. L

    How long does it take for this bucket to empty?

    Homework Statement Ignore turbulence and viscosity. A cylinder with radius r is filled to depth d. There's a leak in the bottom of the cylinder. When suspended from a rope, the depth is reduced to d/2 after 10 minutes. From this point, how long should it take to empty completely...
  41. V

    Is the empty set always part of the basis of a topology?

    The topology ## T ## on a set ## X ## generated by a basis ## B ## is defined as: T=\{U\subset X:\forall\ x\in U\ there\ is\ a\ \beta\in B:x\in \beta \ and\ \beta\subset U \}. But if ##U## is the empty set, and there has to be a ## \beta ## in ##B## that is contained in ##U##, the empty set...
  42. B

    Potential inside sphere with empty cavity

    Homework Statement An insulating sphere of radius R , centered at point A, has uniform chagre density ρ. A spherical cavity of radius R / 2 , centered at point C, is then cut out and left empty, see Fig. (a) Find magnitude and direction of the electric field at points A and B. (b) Find...
  43. A

    Is Cardinality of Empty Set an Axiom or Can it be Proven?

    Is 0 I am told. Is this an axiom, or can it be proven?
  44. MarkFL

    MHB Find Work to Empty Conical Frustum Tank - Juan's Question at Yahoo Answers

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  45. P

    Measuring velocity in empty space

    Let me preface this by saying I know very little about relativity. Last night a friend and I were discussing a particular scenario that will probably arise when humans begin to be capable of interstellar travel. Say you take off from Earth and accelerate to some velocity and then coast until you...
  46. MarkFL

    MHB Kendra N's question at Yahoo Answers regarding work done to empty a conical tank

    Here is the question: Here is a link to the question: Applying integration to physics and engineering? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  47. T

    Does ∅-∅=∅ or does ∅-∅=0? Difference of the empty set and itself?

    I'm having trouble conceptualizing taking the difference between the empty set and itself. There is no element x where x∈∅ and x∉∅, so I'm thinking that it should return ∅ since there are no possible elements. Is that correct?
  48. B

    What is the difference between a null set and an empty set?

    I am a bit confused on the difference between the two. Different sources are giving me different results, so I suppose it depends on context. According to some sources, they are the same thing. According to others, the empty set is a set containing no elements, represented by ∅ whereas the null...
  49. C

    Space as not empty, non-locality, conceptual implications?

    Hi there! I understand the tendency of physicists to stick to the math, and the logic itself, and to often avoid attempting to conceptualize a process or law, but that's kinda the opposite of what I'd like to do here. I don't mind at all if you refer to the theory, math or logic, and id...
  50. A

    Time taken by gas to fill empty vessel

    Suppoese there is a empty vessel connected to a pipeline having a continuous supply of gas at pressure P. Gas will continue to move in vessel till pressure in it become P. How to calculate time required to fill the vessel completely. Plz help.
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