Empty Definition and 271 Threads

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. turbo

    Through what medium does EM propagate in empty space?

    Through what medium does EM propagate in "empty" space? Einstein stated in his Leyden address (1926, I think) that an EM ether was mandatory for the transmission of EM waves through "empty" space. He was unable to reconcile this with the dynamical gravitational ether that had to exist to make...
  2. R

    Pair Production: Why Not in Empty Space?

    Is there a short answer why pair production can not happen in empty space, but that photons must interact with an external field? thanks and a nice weekend oh, just saw someone asked the same question in the nuclei section today and answers already there
  3. H

    Is the Empty Set a Valid Vector Space? A Closer Look at the Ten Axioms

    While reading text, I had a question which I can not resolve by myself. Please Help me! it reads, The empty set( a vector space with no elements) is denoted as & (This symbol doesn't matter for the sake of argument, I don't know how to write the Zero with a line in the middle). I can...
  4. U

    How much work is required to empty the tank?

    need help, VERY CHALLENGING a hemispherical tank of radius 6 meters, is posiitoned so that its base is circular. how much work is required to empty the tank? liquid density is 100 kg/ m^3
  5. C

    How can empty space give off radiation from the Big Bang?

    From what I understand, empty space has a temperature of 2.7 degrees K? And that empty space still gives off micro-wave radiation from the big bang? Can someone help me visualize this? For me, the idea of empty space giving off radiation and having a temperature that isn't absolute zero is...
  6. P

    What is the percentage of empty space in an atom?

    Recently i read: "atoms turn out to be 99.99999999% empty space" (source: http://www.futurehi.net/docs/Reality_Consciousness.html ) Is this correct? Does a more accurate measurement of the percentage of empty space in an atom exist?
  7. P

    Work Required to Empty Tank of Hot Chocolate

    A tank in the shape of an inverted right circular cone has height 8 meters and radius 6 meters. It is filled with 7 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is 1510kg/m^3 m =...
  8. R

    Hawking Radiation – Empty space virtual antiparticle-particle pairs

    In reviewing explanations on evaporating Black Holes using Hawking Radiation, based on how the black hole might treat Quantum “Vacuum particle pairs”. Although direct observation of Black Hole radiation has not been confirmed it implied that “Antiparticle – Particle creation, and self...
  9. honestrosewater

    Is There Meaning in an Empty Universe?

    Do I understand correctly that the universe, x, is empty just in case [\exists x (Px)] is false and [\forall x (Px)] is true? Is there anything interesting about empty universes? I don't have any problems with them yet, but I'm not sure how to think about them. That is, they seem to be lacking...
  10. B

    Magnetic field in empty space?

    I was given this problem to think about from my professor. It's not for any class. It went something like this: Imagine there is some magnetic field in empty space (tightly-packed lines curling around in a circle) at t=0. What happens to the field as t -> infinity. I figured Maxwell's...
  11. Oxymoron

    Intersection of disjoint SETS is empty

    The question is: Suppose W and X are subspaces of R^8. Show that if dimW=3, dimX=5, and W+X = R^8, then W \cap X = \{0\}. I can see this is obvious iff W and X are disjoint sets. If we add members of W to X in the usual way, and we get the new set W+X whose dimension is now 8 (given), then...
  12. J

    The temperature of empty space What now?

    Following Hubble's discovery of the expanding universe, George Gamow postulated that the universe began as a big bang & calculated the temperature of empty space to be around 3 degrees Kelvin. In the early 60's this temperature was confirmed. We now know that rate of expansion is...
  13. S

    Proving the Existence of the Empty Set in Every Set

    When I took a math foundations class we only did naive set theory and took as an axiom that the empty set is a member of every set. The book had formal set theory and thus listed the ZFC axioms. One of them was that the empty set exists and that it was a member of every set. I've looked at a...
  14. Monique

    Empty space can set objects in motion

    http://www.nature.com/nsu/040126/040126-19.html I thought this was interesting:
  15. E

    Solving a Complex Integration Problem: Finding the Work to Empty a Tank

    I apologize that I don't know how to make the math equations. Alright it's going to be kind of complicated trying to describe this in words, but I'll do my best. There is a tank shaped like a right cylinder on it's side. The length of the tank (or height of the cylinder) is 6m, and the radius...
  16. O

    A question about the empty set

    It is very important to define a fundamental concept like set before we use it. The set concept can be useful iff there is clear separation between two basic concepts, which are: container and content. Before we are going to check the ratio between these concepts, we first have to...
  17. P

    Exploring the Boundaries of Empty Space: Does it Go on Forever?

    I suppose this has been asked before, but I am somewhat new to this forum. Beyond our known physical universe, there is a region of "empty space" Fine. And if I were on the "edge" of our observable physical universe, and I traveled faster than C away from it, I suppose I would eventually...
  18. J

    Is gravity being the place that is empty?

    Is gravity being the place that is empty?
  19. T

    Exploring the Possibility That No Part of the Universe is Empty

    I have just recently read a book entitled THE HOLOGRAPHIC UNIVERSE in which it is suggested that what we now call empty space is only called empty because we are like fish that cannot see the water they swim through. Is there a reason to consider that any area of the universe is empty?
  20. E

    Would the concept of empty space exist without depth perception?

    For the past few thousand years or so, the philosophy of space has occupied a lot of time among philosophers. There is really no argument as to the traditional definition of "space" as it usually relates to volume, being length width and breadth. But the big debate has typically been over the...
  21. R

    How does a boomerang behave in empty space and gravity?

    If a spaceship throws a boomerang in the vacuum of the space but with some gravity from earth. Will it have the same trayectory than if you throw a stone of equal mass than the boomerang with equal force? thanks
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