sets

  1. A

    Club Sets and Fodor's Lemma

    I'm trying to obtain a better understanding of what a club set is to get started. I understand what it means for a set to be unbounded with respect to a limit ordinal $\kappa$, but I'm having trouble grasping what it means for a set to be closed in $\kappa$...
  2. I

    Hereditary sets and posterity

    Hi, My question is about hereditary sets and posterity in set theory. The definition of a hereditary set is a set whose members are a hereditary set. I am trying to wrap my mind around this definition. Perhaps I am thinking too hard on it. My understanding is that it is just what the name...
  3. L

    Median between infinite sets

    Is the "midpoint" between the sets of numbers approaching positive infinity and negative infinity definable as the set of countable numbers?
  4. P

    Definition and sets

    The following sentence, a set is infinite if and only if the set have a bijection with itself, the negation of the affirmation is true? A set is finite if only if there doesn't exist any bijection with itself? The idea is what is a better definition of a bijection in this case. (Sorry, guys...
  5. L

    Symmetry between all null and all unbounded sets

    Is there a greatest symmetry between the set of all null sets and the set of all unbounded sets?
  6. A

    Intersection of Two Sets Question

    Does there exist a Vitali set $V$ such that the difference between $V$ and the Cantor ternary set is empty? Vitali set $V$: https://en.wikipedia.org/wiki/Vitali_set Cantor ternary set $\mathcal{C}$: https://en.wikipedia.org/wiki/Cantor_set Equivalently, is the following statement true...
  7. A

    Some Crank Talking About Vitali Sets

    Vitali sets are interesting creatures to me: https://en.wikipedia.org/wiki/Vitali_set The measure of a Vitali set is undefined as clarified above. I assert for the sake of argument that the measure, $\gamma$, must be both greater than 0 and less than all real numbers greater than 0. I assume...
  8. R

    Looking for something like Penner's Easing Functions, but for larger sets of data

    Hey all, I work in CG, I'm a technical director (I help build tools that facilitate the work of animators in 3D animated productions, VFX and the like). We work with keyframes a lot, where we store the transforms of certain objects and parts of characters over time. These keys are represented...
  9. S

    Classes and sets

    What is the difference between a class and a set? Please give some simple examples. I have seen statements like "Let M be a class of subsets of X...", and it seems to me we can still do everything we like as though M is a set, and we are just avoiding the word "set" and replace it with "class"...
  10. S

    How would I solve these questions on Sets?

    Does anyone know where I can answer questions like these? An online calculator or some sort? - Let A={1,2,3,4},B={3,5,7},C={2,3,4,5}A={1,2,3,4},B={3,5,7},C={2,3,4,5} and D={6,7,8} - In the following, you may assume that N={1,2,3,4,....} and Z={...,−3,−2,−1,0,1,2,3,...}...
  11. L

    Count members of all sets of interchanged reals

    What is the cardinality of members of unique sets representing all bijective interchanges among the real numbers?
  12. Chemist116

    How do I find the number of elements in differents sets when the total is not given?

    The problem is as follows: In an institution they offer three language courses one being German, the other French and the last one Polish. Four students enrolled in the three courses, six students in Polish and German and seven in French or Polish. If all students enrolled in Polish also...
  13. L

    Range of Continuous & Differentiable Sets

    Let $f:R -> R$ and $f(x) = |x-1|+|x-2|$. Let $S1 = ${$x| f$is continuous at $x$} and $S2 = ${$x| f$ is differentiable at $x$} then a) $S1 = R , S2=R$ b) $S1 = R - ${$1,2$}$, S2 = R$ c) $S1 = R , S2 = R - ${$1,2$} d) $S1 = R - ${$1,2$}$, S2 = R - ${$1,2$} Which of the following is true ...
  14. L

    Question on Sets

    If $f(x) = g(x)$ $\forall x \epsilon Q$ then $f(x) = g(x)$ $\forall x \epsilon R$ Is this always true ? Since the set of Reals contains both Rational & Irrational numbers, I feel it is not always true. But someone kindly help me with this problem. Thank you!
  15. Chemist116

    How do I find the least number of elements in a series of sets?

    I need help with this elementary set problem it states as follows: In a toddler's room there are 120 toys, 95 of them uses batteries, 86 have wheels, 94 are red color, 110 are made of plastic, 100 emit sound. How many of the toys share all the characteristics? Initially I thought upon...
  16. B

    Strange sup & inf

    Find the sup and inf of this set $$A={ \frac{mn}{1+m+n}}$$ With $m,n\in \mathbb{N}$. (Let be A a subset of $\mathbb{R}$). How to find them? I tried to change the variables, putting $a=n+m$ or $a=nm $ but it doesn't seem to work! Any idea?
  17. Monox D. I-Fly

    International Notations for Number Sets

    Okay, so I know that the international notations for the set of natural numbers, whole numbers, rational numbers, real numbers, and complex numbers are N, Z, Q, R, and C, respectively. However, what are the international notations for the set of integers (natural numbers and zero), even numbers...
  18. O

    The P of the # of two random sets

    I found this question a satisfying challenge, so I hope I got it right! "Let X be a set containing n elements. If two subsets A and B are picked at random, what would be the probability that they are both the same size?" So, basically what is the probability that the cardinality of the...
  19. X

    interesting sets of equations

    in real numbers sets of equations \begin{align*} x^{2}y+2=x+2yz \end{align*} \begin{align*} y^{2}z+2=y+2zx \end{align*} \begin{align*} z^{2}x+2=z+2xy \end{align*}
  20. L

    Cardinality of union of two sets proof

    Hello all I am not able to write a proof of the property n(A \cup B) = n(A) + n(B) - n(A \cap B) . I was just able to draw sets diagram and one or two steps attached. Please help me with the proof.