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. Ranger Mike

    Exploring Zero Point Energy in Empty Space

    Does Empty Space have Mass? Does Empty Space have Energy? from a previous post i learned that energy is everywhere. Even Empty Space. zero point energy. correct? never mind , i found the answers
  2. T

    Batteries connected in Empty Circuit

    Homework Statement Three identical batteries, with finite internal resistance, are connected in series in a closed loop. (Positive Terminal of battery 1 to Negative Terminal of battery 2; Positive Terminal of battery 2 to Negative Terminal of battery 3; Positive Terminal of battery 3 to...
  3. L

    Empty Relations: Domain, Range & Functionality

    What is an empty relation? Can an empty relation be a function? Is an empty relation one with the empty set as its domain or as its range or both? THanks
  4. M

    Can empty space or emptiness conceive a form from which matter arise?

    Can empty space or emptiness conceive a form from which matter arise?
  5. C

    Calculating Work to Empty a Water-Filled Trough

    A trough is 2 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of x^6 from x=-1 to x=1. The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: The...
  6. S

    Is the empty set a compatible subset of a dense set?

    If A is a dense set, then all subsets of A are dense. However, all sets contain the empty set. Is this a contradiction or is the empty set a compatable subset of a dense set? If it is, why?
  7. V

    Is the Empty Set Its Own Element or Subset?

    Hey. um i got a few questions about the empty set... i know for a fact that the empty set is a subset of all any set.. a) but is it an element as well?? b) can it be an element of itself ? c) or even a subset of itself?? example \oslash \in\oslash is this true?? \oslash\subset\oslash...
  8. K

    Elliptic orbit from empty focus

    hello, I am solving a problem about the angular velocity in an elliptic keppler orbit as seen from the empty focus of the ellipse. Homework Statement Show that the angular motion of a keppler orbit as seen from the empty focus is uniform to first order in the eccentricit. The Attempt at a...
  9. F

    Empty lattice energy bands (Kittel, problem 7.2)

    "empty lattice" energy bands (Kittel, problem 7.2) Homework Statement This is problem 2 of chapter 7 in Kittel's "Introduction to Solid State Physics". The student is required to sketch the free electron energy bands in the empty lattice approximation and in the reduced zone scheme, for...
  10. E

    Is the Empty Set Bounded? Proof and Contradiction

    Does the empty set have a supremum ( least upper bound)? if yes, can anybody give me a proof please? if no, again a proof please?
  11. C

    Estimate the velocity and angular velocity of an empty pipe

    Hi, I need to resit some exams and I'v been having difficulty trying to solve this problem. Estimate the velocity and angular velocity of an empty pipe of mass (m)=1000kg, Diameter (d)=10mm, shell thickness (h)=1mm at the bottom of a slope of angle \theta=45^{}o and path length L=5000mm on...
  12. A

    Empty universe except for three indentical planets

    Hi, I would like you people to approach these problem of an infinite universe, which contains only three identical objects, say planets of equal volume and mass at equal distance from one another: Scenario 1) They all hover in the sky not moving relative to one another. Are they all...
  13. S

    Trouble comprehending the empty set

    What exactly is a set with no elements? What does it mean? Aren't sets entirely defined by their contents? In what manner is a set with no contents defined? I'm not arguing for or against such an axiom... I simply want to know what the axiom actually is saying. If an empty set is not...
  14. E

    Exploring the Concept of Open Sets: The Case of the Empty Set

    The definition of an open set S is that there exists, for any point x element of S, an open ball with center x, all of whose points belong to S. But if S is the empty set, then it contains no point. How can we say that the above is valid if there is no point around which to build an open...
  15. J

    Empty Space Just a quick thought you might enjoy.

    "Empty Space" Just a quick thought you might enjoy. I was reading a book on quantum gravity the other day when I found myself having a lot of trouble grasping the idea of empty space. When you really sit back and take it in, it is so weird only because we never really experience it. Another...
  16. W

    Twin paradox in an empty universe

    The obvious objection to the famous thought experiment with one of a twins moving away from the Earth is, couldn't you have moved the twin together with the Earth in the opposite direction to yield the opposite conclusion. Thes standard answer is that the symmetry is broken when the returning...
  17. snoopies622

    Understanding Einstein's Law of Gravitation in Empty Space

    Why is Einstein's law of gravitation for empty space sometimes identified as Ricci tensor=0 instead of Einstein tensor=0. The first condition implies the second one, but not the other way around.
  18. G

    Do Electrons in an Empty Space Still Obey the Exclusion Principle?

    Hi, I understand that electrons in a solid (eg. metal), can be treated as Fermi gas obeying Fermi-Dirac statistics, which incorporates the exclusion principle. This differs from a normal gas because a regular (ideal) gas of atoms or molecules can have atoms occuppying exactly the same energy...
  19. M

    Intersection with empty index set

    If I is empty, and the collection of sets {A_i} is indexed by I, then the intersection of all the A_i is equal to the universal set. Can someone explain why? Or better yet, give a proof?
  20. E

    It's March 10th and my mailbox is empty

    So far in the graduate school application process this is how I stand: illinois (accepted w/o support) Tufts (accepted w/o support) Duke (rejected) ------- Haven't Heard from University of Washington University of Southern California City University of New York Rice University Boston College...
  21. R

    Proving an intersection empty set

    I'm trying to prove \bigcap^{\infty}_{n=1}(0,1/n) = EMPTY SET. One thing that I can't seem to bypass is getting past the closed intervals as stated in the Nested Interval Property, which states "For each n\in N, assume we are given a closed interval I_n = [a_n, b_n] = {x \in R : a_n \leq x...
  22. H

    Electric field in an empty cavity

    Homework Statement The electric field inside an empty cavity in a conductor is zero. Is this statement true no matter what the shape of the cavity? Why or why not? Homework Equations Electric field equation. E = kQ / R^2 The Attempt at a Solution I can't seem to figure out if this...
  23. B

    Mysterious Death: Man Found Hanged in Empty Room

    A man is found in an empty room hanged by a noose hanging from the ceiling, which is the only thing in the room other than himself at the time of discovery. How did he do it?
  24. A

    Help with empty boxesalgorithmic problem.

    Hi, I've been given this problem for homework but I am completely baffled..I can't even translate the first move into values on the variables.. Any help on this would be greatly appreciated..Sorry if I'm being a bit abrupt here but my head is fried at this stage.. Thanks Guys...
  25. O

    Why EFE Satisfy Empty Space in 2-3 vs 4-D+ Dimensions

    Hi I'm a newbie for GR so please answer my basic question in empty space why we say for 2 or 3 Dimensions field equations in that region must have a curvature tensor equal to 0 but when we say about 4-D or higher , the curvature tensor which non-vanish can satisfy EFE? I think when we...
  26. F

    Exploring the Relationship Between Zero and the Empty Set in Set Theory

    My question would be: In mathematics of set, can be 23 a set with 23 elements. Could be 4 a set of four elements? Then would be zero the empty set. And if zero is the empty set, would be 3 emtpy sets equal to 1 empty set.
  27. R

    Is 99% of the volume of the universe empty?

    If you look at the size of the amount of empty space in an atom, compared to the tiny size of the nuclues, does it not mean that the universe is nearly entirely empty? like 99% empty?
  28. B

    Gravity: Is Matter Mostly Empty Space?

    People say gravity is an extremely weak force. Weaker than any of the other three basic forces that govern our universe. Explanations to this have varied in all forms of radical ideas (I'm not saying I outright reject them). But it has always pestered me the idea that perhaps gravity is such a...
  29. N

    What Does It Mean When We Say Empty "Space" is Expanding?

    This was moved from another thread in the relativity forum, as it isn't about relativity - pervect. Hi, I understand your question and your frustration. The problem arises by misinterpreting a mathematical description of reality (General Relativity) by reality itself. The "pure relativists"...
  30. L

    What Causes Voids in the Expanding Universe?

    I know that astronomers have found things like this before, but to find an empty part of space this big really makes you wonder... My question to you all is, what are your theories on why there is emptiness in certain parts of space?
  31. E

    Vacuum in Quantum Field theory is not empty

    I know that the vacuum in Quantum Field theory is not empty, but sometimes I find some people say that the particles are created from nothing because they are created from the vacuum , are those people expression a misleading?
  32. J

    Is Empty Space Just a Bunch of Relationships Between Events?

    I have a question. If empty space is, according to relativity theory, curved, and it is expanding (ie. it has properties) then logically, empty space must be made from "something" right? And this something could be interacted with?
  33. marcus

    Wright's 'best fit' universe does not expand out into empty space

    Ned Wright's best fit standard LCDM is simply one possible concrete version of the usual LCDM model that cosmologists use. It has the normally preferred parameters (0.27, 0.73, 71) plus the estimate that Wright gave of Omega = 1.011. That's what he gave in January 2007 as the best LCDM fit to...
  34. Robert100

    How can empty space expand? (Reality behind the GR equations.)

    How can "empty space" expand? (Reality behind the GR equations.) I have a question - with some concerns over how it may be answered. On other websites, and in other print publications, I've seen Ph.D. physicists and cosmologists misunderstand the question: What does it mean when we say that...
  35. P

    Empty Set Containment: Exploring the Relationship with 0 and the Zero Vector

    Homework Statement Does the empty set contain 0, the zero vector, ... all zero elements of a non empty set? Homework Equations The Attempt at a Solution I don't think so. But could be wrong. The empty set shoudn't contain anything whatsoever.
  36. P

    Can a Complete Metric Space Have Empty Interior?

    Homework Statement Can a complete metric space have empty interior? Homework Equations In mathematical analysis, a metric space M is said to be complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M. The Attempt at a Solution But if M has no...
  37. B

    Proving Subrings: Understanding the Empty Subset of a Ring

    My teacher put heavy emphases on acknowledging that a subset is nonempty of a ring when proving something is a subring of something. For the final exam, she wants to put a question with empty subset of a ring, and do subring proof. The empty subset would have "nice" description so you can do...
  38. A

    Does a Set with Empty Interior Have Measure Zero?

    does a set with empty interior have measure zero? I think it does...
  39. R

    Weight of air-filled balloon vs empty balloon

    Homework Statement Take 2 rubber balloons A and B of equal mass. Balloon A is filled with air and balloon B is left empty and the two are weighed in a pan balance. What will you observe and why? 2. The attempt at a solution The balloon with air will appear lighter if experiment is...
  40. P

    Empty Set & Subset: Does it Sound Right?

    In my book, it says "We agree to regard the empty set as a subset of every set. Thus any non-empty set S has just two improper subsets, the empty set and the set S itself; all other subsets of S are proper." Does this sound right? I thought the improper subset is the set which is the same as...
  41. L

    Why do atoms prefer filled, half filled, or empty shells?

    Why do atoms prefer filled, half filled, or empty shells?? What is the reason for this?? In chemistry, they tell you that atoms are "happier" in these states, but WHY? Nobody can seem to give me an answer. I have a hunch that it has to do with entropy of the various configurations, but can...
  42. T

    Matter/energy in 'empty' space

    I read somewhere the dictum that 'nothing can be done without at least a material base' ; the way the term matter was employed in this text implied that vacuum, 'empty' space, was to be viewed as matter-less. This would mean that in empty space, nothing at all can be done. This leads to an...
  43. D

    Intersection of cosets is empty or a coset

    "Let H and K be subgroups of a group G. Prove that the intersection xH\cap yK of two cosets of H and K is either empty or is a coset of the subgroup H\cap K." I'm stuck here.
  44. A

    What is the projection of the empty set?

    I'm wondering if the projection of the empty set has been defined? several books I've read seem to regard it in different ways
  45. S

    What is vacuum or empty space?

    What is vaccum? Many say its "empty" space. But what does "empty" mean? Does it mean that there are no atoms (or protons/electrons, or quarks, or strings)? Can anyone explain this?
  46. D

    Friedmann Equation and the age of empty universe

    Got stuck in this question, the question asked to use friedmann equation to show that the age of an empty universe (average density = 0) is τ=1/H₀ where H₀ is the present day value of Hubble's Constant. Well, i got the friedmann equation by put the value ρ(average)=0 but the trouble is...
  47. Tsu

    Why Is My PM Box Always Empty?

    Empty your PM box (AGAIN! - sheesh :rolleyes: :smile:) Are you getting spammed again?1111 :smile: :smile:
  48. F

    Answer the Question: Is Completely Empty Room Possible?

    Someone asked me this question and I was wondering how you guys would answer it... Consider a container with some gas in it. It can be a sealed living room filled with ordinary air at typical pressure. The air molecules are in motion - colliding with each other and bouncing off the...
  49. F

    Empty Nest - possible or not possible aspect of Big Bang?

    Hello, I think this is a good theoretical question (hypothetical question) to ask. What I am interested in figuring out is: the possibility of the following hypothesis, not whether it is rejectable or not. Is it possible?? With the term 'Empty Nest' the specific condition and location...
  50. honestrosewater

    Axiom of Empty Set superfluous in ZF?

    Only some versions of the ZF axioms include an axiom stating that an empty set exists. According to mathworld, the Axiom of the Empty Set (AES) follows from the Axiom of Infinity (AI) and Axiom of Separation (AS), via \exists x (x = x) and \emptyset = \{y : y \not= y\}. I guess they think the AI...
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